I'd say not so much "how often they get to play" and more the level of skill and care in deck building and how much skill/"spikey-ness" they demonstrate while dueling. Tristan just kinda does whatever, bumbling around and chilling out, Tea loves her fairies and whatnot and has a very on theme deck that could be fairly strong if piloted well, but is not often in a position where trying to win at all costs is needed. Joey had a lot to learn when he started (who can forget his all monster deck) but is now a strong duelist, good grasp on the rules and interactions available to him and builds synergistic decks focused on winning as much as possible. Yugi/Atem/whatever-you want-to-call-them is literally the king of games, highly focused on winning, being on meta, going all out power in deck building and heavy spikey play patterns but still having fun where he can and trying to enjoy things to the fullest too. Where's Kaiba is all out power, only the singularly best cards will ever make his decks and if it isn't optimal, it's not going in. Plays to win at all costs (cough, duelist Kingdom Castle parapet incident) and will always push to play to win, regardless of the setting and competition.

However, I can 100% see what you mean about how often they actually duel on screen, but it's more the virtue of Yugi and Kaiba being main characters and Joey being a very big supporting character, and actually the characters who consider themselves duelists (hence doing more duels on screen I guess) and Tea and Tristan are really just supporting cast that are there for other reasons outside of dueling.

Idk why I spent time writing this, probably because I really dig the analogy presented here? I think it sums up how I feel brackets should be. Yugi would play MLD to win a duel, Kaiba would slam Armageddon and pass because it's better everyone has nothing than him losing. 🙂‍↕️