Yeah, I'm fortunate myself that while I get to DM Saturdays, I get to also play on Wednesdays in a game DMed by one of my Saturday players. We frequently connect with each other on how things are proceeding so we can build up each other's skills, and we play in each other's games with an eye to how we can help each other move the game forward.
Our combined group (we have 3 games because I alternate Saturday games to accommodate people's variable schedules) includes munchkin players who prioritize how to be mechanically amazing, roleplayers who bind every mechanic to the story they'd like to tell, vibe players who remember about a third of what their characters can do week to week, and one player who simply prefers always to play the "weird" character that most often seems out of place for the setting and group.
Hearing so many people talk about things on this site, you'd think I'd have a group destined to spin out into a controversial split, rather than going strong for 8 years now. We communicate, we don't put our own ideas and preferences above everyone else's, and we prioritize first and foremost the fun and enjoyment of everyone.
And for that "weird" character player, whose preferences are most pertinent to the conversation this thread has become, I am thankful each and every time I've approved it, and deeply regret the one time I vetoed it. Every single time I've adjusted my ideas for the setting and world the group was playing in to accommodate this character, it has 100% led to a much better world and story than I would have otherwise made. The one time I vetoed it was because it was my first interaction with the player and it was my first time DMing. The player was unhappy but did pivot, and later experience proves to me that I was wrong to require it. For the record, the first side game we did, which ended up a full campaign itself, that player got to play their previously vetoed choice.
This is not a blanket statement that every DM should approve every PC always, just that at my table, with proper communication and shared priorities of everyone's fun, I've found that approving has always led to a better experience for the players and myself as DM. I've just found that players who fit the description of problem tropes are often much more than that, and working together builds something better. I'm not de-prioritizing my needs or wants as the DM, I'm incorporating theirs within my own. The more incompatible they may seem, the more creativity may be involved, but every single time, the end result was something I was happier with than what I started with on my own.
My most munchkiny player, as another example, is the best DM's assistant I can ask for. Looking up rules as needed so the game flow isn't interrupted, engaging with the plot and remembering details of the story. My most vibes player loves engaging with NPCs and asking after them, checking in on them. My player who was newest to D&D now has the most powerful character who has dropped more bosses than everyone else combined, which the whole table celebrates and actively makes room to allow them to claim even more kills.