This makes me wonder if this is, in part, a perception problem. The CharOp board is full of powergaming and multiclassing shenanigans, sure, but most people don't play like that. I know of quite a few players who have multiclassed in 3e-based games to fulfill a particular story element or character concept present from the beginning. It's just that the 3e (and later) versions of multiclassing are piecemeal in sequence rather than constantly concurrent which gives the illusion that they're cherry picking rather than fulfilling an important concept. But that's just an artifact of the rules, not really a fair reason to consider the two types of character - a Fighter 1/MU 1 1st level character in AD&D and a Fighter 1/Wizard 1 2nd level character in D&D - different in concept.
It may be that my perception has been skewed by my experiences with it - in the 3.x games I played from 2000 onward the people who would multiclass without optimizing would be corrected by fellow players or have their characters re-done by more mechanically adept players in order to optimize them. So from my experience, most people did play that way, or they would hand over their concept to someone good at playing that way in order to keep them effective enough to play with those who optimized. I'm glad you didn't wrestle with it like I did - and again, I'm not slamming that style - I was always fine to
play in those types of games, but I could not stand to DM them. Particularly in 3e it just wasn't fun for me to constantly approach the next week's game simply trying to create things mechanically challenging enough for the players without gimping their builds rather than focus on any kind of plot/story for them to engage in. Entire classes became useless and unplayable because it was hopeless to put them in an optimized party without having an optimizer player multiclass it into a 'workable' character. It became a race of mechanical one-upsmanship which, frankly, they were way better at than I was, rather than a RPG. It burned me way out - the same with 4e when the hybrid rule presented a similar hurdle.
And certainly, it's not a fair reason to consider a Fighter 1/MU 1 1st level AD&D character to a Fighter 1/Wizard 1 second level character different in concept no, but that's not where I was headed with my wistful remembrances of 1st and 2nd edition AD&D multiclassing - in post-2e incarnations, multiclassing is more about (a 5e example) 2 levels of 1 class to get your path bonus and basic armor and skillset, then switch to your next class for the double attack at 5th level, then back to another class to get x spell slots to boost the one spell that increases damage for your double-attack combo until you have enough slots for that coveted 4th level spell combo, the round out the last x levels to max out your attack bonus, etc. If you consistently go back and forth from fighter to wizard and back again I'd agree with your argument, but we both know that's not really how it really works, is it? Most multiclass builds are designed around you taking a couple of levels of one class to get something, then switch to another class to get something, then back to the first class to optimize what combo you got from the first and second class etc. Additionally a split multiclass in 1e/2e isn't really 1 for 1 - so if you had a 10th level fighter, the multiclassed fighter/magic-user equivalent wouldn't be 5/5 - it'd be more like 8/7 or 8/8.
I try to be a 'yes' DM for the most part - I feel as though saying 'no' to multiclassing to an individual allows me to say 'yes' to the group more often, because I'm looking at the group as a whole and designing based on a system more easily balanced for using the base classes as written, as opposed to trying to re-balance to make things work for one or two people who have optimized using the multiclassing rules and yet keep things from overpowering two or three others who haven't. It's not like I'm rubbing my hands together and cackling about it - if you're a DM who loves to handle that stuff and can do it better than me then you're awesome and I say have at it. But honestly I haven't gotten any argument from my players about it... no one has accused me of trying to steal their fun away or being cruel bastard yet. At least about that anyway. ;-)