I'm not a huge fan of multiclassing as a DM for a couple reasons (which have nothing to do with the rules for multiclassing themselves.)It's why I never understood the resistance to multiclassing. I'm not a fighter or a rogue, I'm a mercenary ready to work for the highest bidder.
One, multiclassing tends to depower a PC a bit, and I don't want my players to ever feel like they are below the curve. Usually if a player wants to multiclass it's because they want a specific game mechanic for their PC and multiclassing is the only way within the printed rules for them to get it. For instance, the Cleric who wishes to dual-wield because their deity does, but they can't get the Two-Weapon Fighting Style without multiclassing (or at least they couldn't before they added the feat in Tasha's). Ordinarily they'd have to postpone their spellcasting a level in order to just take a level in Fighter for that one mechanic... but because I never want to do that to my players I always let them do feature swaps instead. That way they can remain Cleric for their entire career, while still getting Two-Weapon Fighting Style to keep their dual-wield combat power online. I will always default to doing feature swaps over multiclassing whenever possible.
Second, with the size of my games in terms of player count... multiclassing tends to just create overlaps in niche rather than filling holes (which I think is oftentimes what multiclassing is good for.) If my tables were only four players, someone deciding to multiclass to Rogue because the group wanted a PC capable of doing rogueish things would be useful and helpful. But at my tables-- where I'm running six, seven, eight PCs-- there's usually no hole to fill, and thus that multiclass will just water down the PC who does it, duplicating a niche already filled. Thus they will usually be less well off as a character, with new additional features that won't often get used because there's a more effective PC at the table. So I make sure to always point this out to the player before they do it, to make sure it's something they are okay with.
That being said... if it makes sense narratively within the story for a PC to multiclass and the player goes into it knowing the mechanical pitfalls that often come with it... I have no problem allowing them to do so if they are happy with it. It's never my first choice to get the player what they want for their PC, but I'm fine with it if they are.