I think Civilization made a very bad design decision in terms of air units. It appears their idea of air unit is counter versus ground. That's totally wrong. Air units are made to counter ARTILLERY because artillery is the most devastating weapon ever designed in the history of war in terms of number of kills. If you play any reasonable designed wargame, or even just Civ itself you'll see that when you got this unit that can fire from the safety of your own territory repeatedly turn after turn, of course it's going to rack up the most number of kills. In People's General the US artillery units can hit like 10 hexes across while a tank can only travel 6-7 hexes a turn so you can actually fire twice before anything even gets close to your artillery even if there is no other obstruction in the way.
WW2 era bombers use 500 KG bombs. You can put more explosives on a car easily. Of course you driving a car with 500 KG of explosives probably won't get very far which is why it's needed, but in terms of doing damage to ground units there's no way a 500 KG bomb is better than even a bazooka let alone say the Panzerfaust. Advanced Daisenryaku gives a 120 anti-tank rating to Panzerfaust while 50 to 500 KG bombs, and Panzerfaust is on every infantry unit after a certain age which costs like $200 compared to bombers that generally are $2000+. Sure Panzerfausts have like no range but if you got a few million of these weapons somebody's got to be able to get close enough to use one. I mean sure you do drop bombs on ground units just because you might as well use your bombs for something but aerial campaigns aimed at causing widespread destruction is actually pretty ineffective unless you have absolute air superiority.
And the whole notion of eliminating the turn the bomber 'returns' to resupply which they used to do in Civ 2 completely skews the balance. You don't necessary have fighters because they're a cost effective counter to bombers. Again it's much cheaper to load up people with Stingers and just shoot a couple hundred of these in the general direction in the general direction and figure at least one will hit and it'll still cost way less than the cost of say a F22 Raptor. The problem is that someone isn't going to chase down a bomber on a jeep with a Stinger so you kind of want your fighters to both intercept the bombers before they reach the target, and be able to pursue them after they bombed their target. If you're talking about just the actual fighting during the part the bombing takes place, ground units are way more effective at shooting bombers in any era. This is why trying to bomb Syria or Iran is going to be extremely problematic because while their Air Force is no match for that of US, they got more than enough ground units to cause serious losses.