It very much could be done, you dont have to ruin the game's feel either.
The question is, would the changes to the game be appealing to those playing it or put another way.
Do 5e players even care?
The question is malformed.
Do absolutely all, literally 100%, care? Hell no. Certainly not. It's incredibly rare to find
anything that 100% of a large population (say, 100k+) feels the same way about.
Do
some care? Hell yes. We wouldn't have these threads--nor things like PF2e or 5.5e--if nobody cared ever.
And distinguishing the difference is extremely hard without actual, well-made surveys (something even WotC struggles mightily with...) and serious statistical analysis (something I am skeptical at best that WotC ever does, given their total lack of STEM-trained staff.) But even
with those serious setbacks, WotC knows quite keenly that there are plenty of classes which are "popular" yet "unpopular"--because "popular" is a squishy term that means different things in different contexts. The Champion and Berserker are widely-played ("popular") subclasses, but they both have abysmal player satisfaction ratings ("unpopular.") Ranger is a "popular" (widely-played) "unpopular" (low satisfaction) class.
Given these (sub)classes are well known for being on the weaker side? Yes, I think we can say with reasonable confidence that players DO care. They may not always know why; they may not always be able to point to the specific thing that is wrong and say "fix that. That is what I don't like." But they
do have a sense for whether something actually fits within a reasonable balance range--and they've pretty clearly indicated there's a problem to be fixed.
Which is why I maintain that many, many problems with "too much balance" are a matter of presentation, not practice. Things that look familiar, and 5.0 was
very very conscious about looking as familiar as possible aka as close to 3.x as possible, will get a good initial reception, even if there are underlying problems that simmer below the surface and require surveys to reveal. Things that look unfamiliar,
even if they are well-made, will get at best a chilly response and at worst outright hostility, so you never get the chance to see the long-term response.