If this happened, almost everybody would dump int.
It's already the case almost everybody dumps int.
Int just doesn't do a lot other than give you reason to know some things in-character you could probably work out with the correct spell from your wizard, anyway.
It's boring.
I dump dexterity because it just feels less boring, and I don't have to either pretend to be dumb/bad memory or forego it and do bad roleplaying.
So, yes, anybody who can use heavy armour can dump dexterity.
However, they're still penalized - dex saves are more common than int saves. A lack of stealth, and a lack of initiative. Still, that's not a massive price to pay.
If you wanted to metagame a lot, tanks would usually have low strength high dexterity (save for barbarians) because if you use a shield, there are no stronger one-handed weapons than a 1d8 - what the rapier is. You lose 1 AC for going studded leather + 5 from dex or half-plate with + 2 from dex. You can use dexterity on ranged weapons, too.
So, currently, you can kind of dump your dex. If your DM constantly makes you fight without armour, however, you're kind of fucked.
And that isn't really fair, when what you're doing is adding attribute diversity to the party.
Yes, I am making a big deal over nothing. Usually it's nothing.
But I don't want to see DMs actively encouraging that everybody takes dex.
Because the unfortunate truth is, dex and con are always good stats on everyone. Int and str are rarely as good.