Why is multi-classing still a thing? I understand it's possbile to meta-game some unique gimmick or combination, but at that point are you really "roleplaying"?
It really seems like you answered your own question... As a DM of 20 years, like you say, I presume you have considered that people may wish to multi-class for.... you know... Roleplay reasons - outside of any meta, because it is what makes sense for their character and the journey they are going through.
From a power and balance perspective, 5e is, of all D&D systems the one that it is least likely to leave you with a broken or underwhelming character. In most previous editions, inopportune multiclassing could lead to an extremely gimped, weak or even borderline non-functional character that couldn't cut the mustard or hold up their part in a team. This is quite pointedly
Not a risk in 5e, because the multi-class system has been carefully designed and implemented to ensure that no matter what class combinations you end up multi-classing to, the overall game system ensures that your character will still be a functional member of the group and able to hold their own and contribute meaningfully. 5e actually does his better than any previous edition... Will it be munchkin optimal, most likely not... but it won't be crippled, and if looking for that munchin min-max is the kind of thing your players
Do look for, there are indeed some very potent multi-class combinations that achieve this.
In short, no, it would be an incredibly short-sighted and stupid idea for a new edition to remove multi-classing rules.
