Is it a problem if a race/class is popular, with a high degree of satisfaction, but mechanically weaker than less popular options? Making the cool race/class more mechanically equal will result in it being even more popular and over-represented.
That doesn't actually track/work logically, sorry.
As I've said, the reason Fighters (and as
@EzekielRaiden pointe out, Humans) are popular even when they're mechanically weak is essentially the aesthetics/concept. When they're mechanically strong, they're not significantly more popular, because they're already popular. As I noted in my post:
Whereas if they're mechanically great, whilst it clearly improves their representation by a some percentage, it's not going to make an unpopular race or class, popular.
The percentage increase I'm describing is typically very small. A class in WoW that's popular due to concept/style but mediocre but then becomes strong might go from 10% of all characters to 10.8% of all characters, or at an extreme, an class that's been weak for years and suddenly becomes outright overpowered might go from 8% of all characters to 11%. Whilst that's a large percentage increase in a sense (like 40% I think), in real terms it's not meaningfully pushing aside other options.
So no, it won't become meaningfully "more over-represented". It's not worth worrying about. Making the class better-designed will be much better for the long-term health of the game than keeping it poorly-designed solely for the sake of
Also, as
@EzekielRaiden points out, popularity and satisfaction are extremely different metrics. If you've played RPGs for a long time, and with a variety of people, I have no doubt you've come across players who play classes even though they don't satisfy them mechanically/gameplay-wise, because they like the concept. I had a player who played Thieves/Rogues solidly through from the beginning to 2E to the end of 3E, and it was only 4E, when Rogues became total badasses, that he realized what he was missing, that a class could truly be fun to play.
That changed him as a player. Have realized classes could actually be fun, he rapidly got bored with the 5E Rogue (which is a fine but "meh" class, at least it's not as hugely lacking outside combat as the Fighter, it's just a little dull - though I feel like some recent subclasses help), and finally broke out and started playing other classes.
But I have another player, one who only plays Fighters, basically. He'd always prefer to play a Fighter, but again, after 4E, he couldn't "go back" to the simplistic design. He played a Fighter in 5E for a long time, but his satisfaction with it, even trying different subclasses, has been low. Right now, I'm not running 5E (I am playing it though), and he's playing a Barbarian. Not because he wants to, but because at least it's not just a Fighter that's a disappointment. I don't think his satisfaction is all that high with that either, but...
Now, I realize someone is probably thinking "this is awfully convenient to Ruin's argument", but it's actually kind of the inverse. I'm arguing this
because my players showed it to be true. Because they don't like how much they lost in their favoured classes just to make fit the "apology edition" criteria. It wasn't really an issue I hugely cared about in 3E (where the gross imbalance of LFQW and the problems caused by PrCs and an oversufficiency of Feats - particularly tax-like ones - were my main concerns, as ENworlders from back then may remember).
5e doesn't answer questions like this. It places the responsibility for encounter balance, combat options, and skill usage in the hands of the DM (for better or worse).
Sure it does. It just doesn't give an attractive answer. Fighters, for example, are fundamentally badly-designed. There's no "DM's responsibility" to fix that. This is an extremely popular and extremely expensive RPG, with reasonably well-paid full-time professional designers. It's one of the very few in the world (and my understanding is it pays drastically more than other RPGs with full-time designers, perhaps even videogame money). There's no excuse for designing a "three-pillar" approach to gameplay, then making it so the Fighter is largely useless in two of those three pillars. It's not like Wizards are largely useless in combat for example, is it? Something as simple as giving the Fighter 6 skills, and say Expertise in a couple of skills, or some sort of ability to analyze enemy weapons and tactics outside combat would have been huge. But instead, Fighters just get to be objectively worse than other classes.
And what you're suggesting is far, far beyond even the wildest stuff the (admittedly terrible) 5E DMG suggests. That's not something a normal DM is likely to come up with.