Depends. There are two separate issues here.
The first is the one I outlined above- that is to say, the "characters as characters" contingent. This wouldn't solve the problem, as they would still complaint about people who weren't even trying to play to their ability. However, it might mollify them somewhat only in that Intelligence was no longer a dump stat for most characters (for whatever reason, a 12 intelligence, say, is different than an 8 when it comes to believably ... I'm not defending the position as internally consistent, just describing what I've seen ... the difference between good at tactics and, um, "Goodbye mama, now you can have ice cream in heaven! I'll see you again tonight when I go to bed in my head movies. But this head movie makes my eyes rain!").
The second are more rules-oriented, and just don't like having a single stat for dumping. This dovetails with my observation of Charisma creep; mechanically, charisma and dex are useful for everything, while intelligence and (to a lesser extent) strength aren't.
Yup. I agree.
It just boils down to what % of the whole the two camps are.
If the latter are the majority, then "much" would apply. If the former, then "not so much." But, it would still be "some."
I would be interested in hearing their position if such a change were to take place (in light of the fact that Intelligence as mechanical arbiter would now probably pack more process simulation punch than all the other statistics...certainly well more than Strength). A PC with Int as dump stat would now be eating:
a) Negative to Initiative (in Rocket Tag, short combats like 5e, that is a significant impact).
b) Suffering in a key Saving Throw (if Int saving throws were made more prolific, they would surely be bad status effects).
c) Suffering Disadvantage on a few Ability Checks per day at GM's discretion (especially crappy if its on shtick/niche Ability Checks).
That makes "oh yeah and you also have to intentionally be all HERP DERP when we're solving puzzles and engaging in strategic discussion (an essential component of the classic D&D experience)" less tenable from both a social contract perspective and a game design perspective. "Hey Patty, remember how you used to have to intentionally HERP DERP, how that intentional HERP DERPING was supposed to somehow not impact your immersion (HERP DERPING for HERP DERPERS is natural, not willfully mechanized), and through that HERP DERPING you weren't allowed to engage in seminal components of play? Well, we're cranking the HERP DERP up several notches! Enjoy!"
This is, of course, compounded (as you note) with its internal consistency already wobbly given the D&D Ability Score model's (specifically, and D&D mechanics generally) inability (you can thank me later for that one) to coherently model biological/psychological processes...compounded further again by its arbitrary granularity in some areas and arbitrary abstraction in others.