Sounds like a guy talking about the good old days except he wasn't even there at the good old days to start.
The most unique thing about FF6 characters is their desperation move which is entirely possible to never see in a casual playthrough of the game since they're very rare. There's really not much individuality except some people's specials are much stronger than other's (Sabin, Edgar, Celes) and Gau's speciality is a nightmare though way overpowered (Catscratch is likely the first attack you can use that will hit 9999). Although the magic-based character in theory have significantly higher magical stats which leads to specialization, the problem is that 2 of the primary magic characters can wield the 'big swords' which will hit for 9999 anyway (Atma Weapon, Ragnarok, Illumina). In terms of playing all you need is Terra/Edgar/Celes/someone else and in terms of story it's almost the same because most characters really have no releveance to the story especially after the World of Ruin. FF6 is very similar to any Touhou game in the sense that characters have depth by music theme. If you write out Rachel's role in the story it goes like this:
"Locke's childhood sweetheart who tried to save Locke (who didn't need saving), lost her memory, later died, was resurrected, and died again so Locke can move on with Celes"
But Rachel's theme is Forever Rachel (which is really a variant on Locke's theme) and it's actually really good, so she is usually thought of as a very good supporting character that is important to moving the story forever, even though there really isn't that much about her. It's funny since the only guy who really has beef with Kefka is Cyan but he's more like a punchline with Gau than a main character. It's the standard problem all FF games suffer until FF10 in that Square never figured out how you're supposed to have a cast with as diverse background even have meaningful things to say without making it look like ad-lib. If your party is Shadow/Relm/Setzer/Mog what meaningful thing can this party possible say relative to the world? Though it's kind of convenient that Terra, Edgar, and Celes are all powerhouses in terms of gameplay so most likely you'll have a party consistent of characters that are actually relevent to the story.