I have heard a few (very few) players talk about balance and imply that they might like a more balanced game, but I have never actually seen that displayed in play.
Come by and join us sometime, then.
There are numerous posters here on EnWorld who expound the same experiences I do, so whether you've seen it or not, it's out there.
I have a big aversion to the DM "putting his foot down" on anything. If you players want that option and it is in the rules why take it away from them? How is the game improved by telling players "you can't do that". This is especially true if it was not stated in session 0. If the DM says in session 0 - no multiclassing or even if he introduces a homebrew where you have to progress both classes, that is fine .... and most players who want to build this type character will simply find another game. But it is not right to literally change the rules on the fly because you don't like the options a player chose.
The DM has all the power levers and can challenge any party with any gear or any options, so I don't see how this is something bad.
Yeah, the bolded part is very true. Establish your rules for running the game from the beginning. Multiclassing is optional, and about half the groups use it IME and from the polls, etc. I've seen online. The ones who avoid it do so because it is easily abused. Feats are much more commonly used in the game, with over 90% of groups using them, even if some nerf or restrict some feats.
But advancing in both classes is a great compromise IMO and one I encourage if players want to multiclass. You are giving up depth for breadth, giving yourself more options but not quite as much power. My preference is for no more than a 2:1 split. For example at 3rd level (becoming 2/1), and by the time you reach 6th you have to be 2nd level in the other class (4/2 or 3/3), etc. so by the end you are have at least 7 levels in your "lesser" class (13/7).
But dipping for just 1 or 2 levels and then leaving a second (or more) class behind is abusive. Those levels are feature rich, with baseline features which tend to be strong. Also, with subclasses and feats, multiclassing really doesn't need to be a thing in D&D anymore. Now,
dual classing, abandoning one class and "forever" progressing in a different class? Sure, that makes sense--people change "careers" all the time after all. But this carries the same rule as multiclassing at a 2/1 or closer balance. For example, you go to 7th-level Rogue (for Evasion!

) and then decide to pick up a level of Sorcerer to augment your Arcane Trickster subclass. Well, you are going to 3rd level or higher in Sorcerer before you can advance your Rogue again.
For myself as DM or player, those are basically my rules for multiclassing.
So, yes, the DM has all the power levers--and this is one of them. Dipping does not, IME, have anything to do with character development so much as power-gaming and optimization, getting some "cool-combo" or syngery with your base class. There's nothing wrong with that, in and off itself, if that is the type of game you want to run or play in, but it isn't to my preference and I've played with, heard of or ead about
way too many DMs who feel more or less the same.
Remember, the game
IS about having fun, but
that includes the DM as well as the players. For some reason, I feel like people keep forgetting that... Otherwise, for players who want to dip in multiclassing, they can either abide by the DMs preferences or move on if they can't accept it. It comes up often enough on the forum: why should the player have to compromise? Well, why should the DM? After all, they are playing, too.