The thing is, any game can be played with homebrew, if the player and GM know it well enough. Hell, some are probably easier to homebrew than D&D. If you want to go through the undertaking of making D&D classless, then go for it. It'll be hard, but some people like the challenge. The crux of the matter is that classless systems aren't inherently superior in any way, nor are class-based systems. They each do what they're made for well, and they all have their fans. I can't imagine D&D moving away from a class-based system, since it's so tied into the DNA of the game. If they did try to go classless, then I'd imagine fans would have an outcry. A not unreasonable one either.
Speaking for BG3 specifically, maybe someone will mod it the way you want, but I can't imagine Larian removing the class system themselves. Firstly, because I'm not confident Wizards of the Coast would let them make such a drastic game. Completely removing the class system would probably go too far in changing the system for their liking. Secondly, that is a major change to try and implement this far into the process. A lot of stuff is already tied to classes, like dialogue options for example. Furthermore, they'd have to figure out how to justify certain classes abilities being included at all. Because for a lot of classes, they come with an inherent background lore that ties them into the setting. How would you become a paladin for instance? Or a cleric and learn those healing spells? What about being a monk once that becomes available? Monks are about more than just punching. There's a whole spiritual aspect to them as well. Hell, even being a druid would present difficulty, despite us meeting a circle of druids, since within the lore, it takes time to train, and an implication that you buy into druid faith.
