I've noticed that games try to go this route rarely ever works, even though this is a staple in virtually anything that remotely features strategy elements. I'm not saying you can't have things that counter certain things, but if you're talking about a strictly rock paper scissors system where A always beats B which always beat C which always beats A that works. Beyond being too simple and just turning everything into a 'if you see B use A', it's usually too simple and not reflective of whatever they're trying to establish. Let's take wargames since those have the easiest parallel. There really was never a rock paper scissor model in war. For the most part ranged units always ruled war (I read that Artillery is responsible for more death than all the other weapons combined in history). If you got a bow you're usually a lot better off than the guy without the bow, not to mention you can still carry a sword on the side at the same time. The guys on the horse/tank are usually way better off than any guy who isn't in one of those things.
The balancing factor should be COST, not something you saw in a movie somewhere that tells you Pike > Horse. Horses are expensive to raise (they eat more than the average human does), and tanks are a lot more expensive than a car to build. This is something that's always problematic with the later Civs where they sort of just homogenize the cost of any military unit to be roughly the same (and the earlier Civs you just use the same type of unit). I guess you're loosely supposed to have like melee > anti horse > horse > melee except it doesn't work half of the time and anti-horse units tend to be your main unit for a significant part of the game. If you take ROTK 11, which starts with the same model (horse > halberd > pike > horse), you'll quickly find that it's really (horse > bow > all, except on rough terrain), but horses are extremely expensive, easily 2-3 times more expensive than any other unit in the standard mode and still about 50% more expensive in the expansion even if you research horse breeder under tech and it leaves you off from other interesting tech you can get instead. So basically two armies almost always start off with only horses and the side that runs out of money will start replacing horseman with pikeman because pikeman are cheap, and this usually lets you at least defend even if you're slightly behind. Occasionally you'll be able to fight in rough terrain where you can actually win, but for the most part pikeman versus horseman is a matter of attrition. After all Pikeman have no possible way to pursue horseman, so unless you got a complete trap in rough terrain, usually the most you can do force the horseman to retreat but since moving units is costly, that might be all you need to come out ahead in resources. If you actually fight head on, horseman usually take less losses even against their counter unit, but since horseman are extremely expensive, it's still okay. Of course the guy with more money than you might decide to make some equally cheap halberdier for your pikeman, but then at that point you'll go back to bulding horseman that tears up halberdier and have no obvious weakness. And if the guy has so much money that he can just keep on building Horseman, you're probably already doomed since he'd have more than 3X your economy to pull that off.
In Daisenryaku for the Sega Genesis, the rock paper scissor model is roughly tank > anti air > helicopter > tank. There are a few uber units like battleships and F/A18 that pretty much are > all but they're stupidly expensive, you'd never be able to field them in any meaningful numbers unless you already have the game won. Additionally infantry pretty much counter everything but tanks cost effectively, since it costs next to nothing to recruit a guy and give him a Stinger, even though infantry absolutely won't close to trade numbers with helicopters but we're in a world where we've no concern for stuff like popular opinion of sending entire battalions to their doom against a superior air force. For the most part the game boils down to amassing tanks because if you ever build a lot of helicopters you know you can't possibly push into enemy territory to them because you'd just see a swarm of infantry with Stingers come out to defend it, but of course you don't want to just get into a tank war if you're against someone with a better tank than you (USA, for example), so you'll see force composition change depending on how deep or not you're fighting at someone since infantry are dirt cheap but takes a while to get anywhere, so if you're on the defense you can build helicopters knowing their infantry won't be able to shoot it down, but if you're on the offense you got to build more tanks because eventually you'll see a bunch of cheap infantry with Stingers showing up. Sometimes you can get cute with Fighter/Bombers but besides being vulnerable to anti-air, they're even more vulnerable to the Stinger swarm since jet planes are way more expensive than anything besides ships and it doesn't take too many Stingers to shoot them down (which I think is even correct).
It should be perfectly viable to amass whatever your most capable of unit is, and the only thing that stops you should be the cost. Amassing tanks does work in real life as long as they're reasonably supported. What stops you from doing this should be the economic aspect of the game, not strategic.
The balancing factor should be COST, not something you saw in a movie somewhere that tells you Pike > Horse. Horses are expensive to raise (they eat more than the average human does), and tanks are a lot more expensive than a car to build. This is something that's always problematic with the later Civs where they sort of just homogenize the cost of any military unit to be roughly the same (and the earlier Civs you just use the same type of unit). I guess you're loosely supposed to have like melee > anti horse > horse > melee except it doesn't work half of the time and anti-horse units tend to be your main unit for a significant part of the game. If you take ROTK 11, which starts with the same model (horse > halberd > pike > horse), you'll quickly find that it's really (horse > bow > all, except on rough terrain), but horses are extremely expensive, easily 2-3 times more expensive than any other unit in the standard mode and still about 50% more expensive in the expansion even if you research horse breeder under tech and it leaves you off from other interesting tech you can get instead. So basically two armies almost always start off with only horses and the side that runs out of money will start replacing horseman with pikeman because pikeman are cheap, and this usually lets you at least defend even if you're slightly behind. Occasionally you'll be able to fight in rough terrain where you can actually win, but for the most part pikeman versus horseman is a matter of attrition. After all Pikeman have no possible way to pursue horseman, so unless you got a complete trap in rough terrain, usually the most you can do force the horseman to retreat but since moving units is costly, that might be all you need to come out ahead in resources. If you actually fight head on, horseman usually take less losses even against their counter unit, but since horseman are extremely expensive, it's still okay. Of course the guy with more money than you might decide to make some equally cheap halberdier for your pikeman, but then at that point you'll go back to bulding horseman that tears up halberdier and have no obvious weakness. And if the guy has so much money that he can just keep on building Horseman, you're probably already doomed since he'd have more than 3X your economy to pull that off.
In Daisenryaku for the Sega Genesis, the rock paper scissor model is roughly tank > anti air > helicopter > tank. There are a few uber units like battleships and F/A18 that pretty much are > all but they're stupidly expensive, you'd never be able to field them in any meaningful numbers unless you already have the game won. Additionally infantry pretty much counter everything but tanks cost effectively, since it costs next to nothing to recruit a guy and give him a Stinger, even though infantry absolutely won't close to trade numbers with helicopters but we're in a world where we've no concern for stuff like popular opinion of sending entire battalions to their doom against a superior air force. For the most part the game boils down to amassing tanks because if you ever build a lot of helicopters you know you can't possibly push into enemy territory to them because you'd just see a swarm of infantry with Stingers come out to defend it, but of course you don't want to just get into a tank war if you're against someone with a better tank than you (USA, for example), so you'll see force composition change depending on how deep or not you're fighting at someone since infantry are dirt cheap but takes a while to get anywhere, so if you're on the defense you can build helicopters knowing their infantry won't be able to shoot it down, but if you're on the offense you got to build more tanks because eventually you'll see a bunch of cheap infantry with Stingers showing up. Sometimes you can get cute with Fighter/Bombers but besides being vulnerable to anti-air, they're even more vulnerable to the Stinger swarm since jet planes are way more expensive than anything besides ships and it doesn't take too many Stingers to shoot them down (which I think is even correct).
It should be perfectly viable to amass whatever your most capable of unit is, and the only thing that stops you should be the cost. Amassing tanks does work in real life as long as they're reasonably supported. What stops you from doing this should be the economic aspect of the game, not strategic.