I think Avatar specifically works because the way it does its worldbuilding fits
really well with how Magic has historically done worldbuilding, which is that it tends to revolve around broad factions with most legendary characters being exemplary of the faction they're from.
Take Stitcher Geralf as an in-universe example - within the context of Innistrad, he's not terribly exceptional in the grand scheme of things. Sure, he's good at stitching corpses together into zombie monsters, but that's something that people can just
do on Innistrad (to the point where you can make "necromancer" a
backup job). What makes him a fun character is his
incredibly catty relationship with his sister - both of their styles of necromancy are involved in their spat, but you're given a sense that "two siblings squabling over the best approach to making walking corpses" is just a
thing in Innistrad.
Similarly, Iroh isn't a fun character because he can conjure and control fire using kung-fu, because that describes a large portion of the culture he comes from - no one in Avatar is
remotely surprised that firebending exists. What makes him fun and endearing is that he's a wise old man who loves tea and acts as a counterweight to his more fiery nephew. So you end up with a fun character that people like that also tells you "hey, cool fire powers are just a thing that people have".
Why this is important is clear if you think about it from a draft perspective - if you draft some firebenders and then see
Uncle Iroh in a pack, you go "oh, look, it's a special fire guy!", which gets built on by seeing cards with quotes from him or cards showing him doing stuff that isn't an expected Cool Fire Dude thing (like running a tea shop). It also works in reverse - if you run into Iroh first and then see firebenders, you get the "oh wow, being a cool fire dude is normal here, that's cool" vibes that help sell you on the setting. Having repeated setting details helps build the whole thing into a more cohesive whole.
Contrast that with Spiderman, where the specific characters you're presented with are either a mass of "spider heroes" that you're assured are all
super special but don't have a benchmark for if you aren't a pre-existing spider-fan or are a one-off villain that doesn't connect into anything else. If you don't go into the set with spider knowledge, the mechanics are left to carry everything because the themes simply don't cohere, because every single legendary creature is trying to be a special snowflake when a draft set can only really handle a couple weirdo outliers. "Oops all the legendary creatures!" should be a precon thing, where people can skim through the cards and see everyone in context.
tl;dr: Magic traditionally uses characters as the flavor/vibe equivalent of a draft signpost, and Avatar happens to work pretty well in that style.
...
That said, I feel like they kinda shot themselves in the foot by deciding to give each major character multiple legendary creature cards showing them at different points in the story. I kinda get why they did it, but I feel like it'd be much more effective if, say,
The Art of Tea replaced
Iroh, Tea Master in the main set. Show me that Iroh loves tea, WotC, don't tell me!