Hiya!
A couple of points from my perspective.
(1) Not allowing 5e MC'ing isn't the equivalent of "eating the same food all the time" if it's "burgers". I'd buy an analogy of "eating the same food all the time" if it was "western cuisine". Someone who has a free-for-all, anything goes type of campaign reminds me of a movie where a bad guy is trying to entice a bunch of kids to do what he/she wants. There is a HUGE table, filled with...
everything....hamburgers, pizza, duck, turkey, soups and stews, hagas, pasta, cupcakes, sugar-coated plums, ham, steak, potatoes, etc, etc, etc. To me, that's the feeling I get when a DM (say, Pathfinder or 3.x in particular) said "Play whatever you want from any book". I had no idea what to do. There was no theme. There wasn't even a hint of cohesion. It felt...pointless, I guess.
(2) Just because I don't allow MC'ing in 5e doesn't mean I'm opposed to it (Multiclassing). I have no problem with the idea at all. My problem stems from my personal hang-up about a PC never actually "being" his classes. He's one of them, and only one, and maybe only one he
isn't even actually trained as yet. A Fighter who gains 300xp and then wakes up in the morning and exclaims "Hey! I can cast wizard spells now, just so you all know" doesn't make a lick of sense. It totally kills any sense of the campaign being a logical, reasonable fantasy world. Effectively, that Fighter didn't learn ANYTHING, except the ways of magic, which he didn't actually DO ANYTHING RELATED to magic. Zero sense. Because of this, the whole 3.x style of MC'ing, IMHO, is just dumb. And, just as unfortunate, players seem to take on this mentality as well. If a DM, such as myself, was to inflict grievous rule-wounds to how one would go about becoming MC to a player who was "used to" the 3.x/PF/5e style of MC'ing (re: just "take a level dip in [class]")... many kittens would be had! The player would be screaming about how "unfair" I am, or how "pointless" it is to MC, or how the game will suddenly "suck" and be "stacked against the players". As I said...they'd loose their kittens. Easier to just say "No" and then hear a bit of complaints, then get on with the game, rather than hear a never-ending stream from players about "how cool" their characters would be if they could just multiclass as Bard/Warlock/Sorcerer and maybe take a level dip into Fighter just to get all the armor and weapons...and hear that
every time they leveled up.
(3) Its my game, my campaign world, my rules. It's as simple as that. Yes, I do listen to my players, and yes I do acquiesce to their requests sometimes. But it's
my responsibility to maintain a cohesive, believable, and fun campaign. It's like dealing with teenie-boppers at a long-weekend camp out. You can't just "let them do whatever they want" because chances are you'd be going to court or jail when you got back. You have to allow them to explore (for self confidence and independence), learn, take risks (so they can learn consequences), AND have fun. But if you just let 'em have whatever they want, whenever they want... it will
not work out in the long run. Just like letting your players dictate what is/isn't allowed in the campaign "just because they like something". IMHO, the CAMPAIGN comes before short-term player happiness. I'm probably going to get yelled at for that, so go ahead. All I know is that I've had several multi-year (over a decade, in one case) campaigns with this crazy hobby called "Role-Playing", with pretty much the same player base (in different configurations). And if I can still be such a "self-centered hard-ass DM", and still keep players engaged and coming back for more for years and years (and decades!) on end...well, I must be doing something right!
^_^
Paul L. Ming