I don't follow. Such a character would have a damage output very close to that of a strength-based greatsword user, which balances their slightly-higher AC.
They won't have access to GWM so damage would be a bit behind a greatsword user and a dex sword and board fighter has better initiative, ranged options, and skill choices.
The popularity of the dexadin points to how backwards the system is - at the very least a rapier should have been a 1d6 and light (yes, that just makes it a shortsword - they don't both need to be in the game).
I suppose it isn't as big of a deal for rogues, if we expect they can perform a sneak attack every round forever; but it's even more of an issue for monks, who scale by number of attacks.
That they designed in to the game. If there was a monk-specific problem, it should have had a monk-specific solution. Instead strength is a dump stat for many (perhaps most) melee characters. That's weird; and with the way acrobatics works, having a 10 strength and/or no proficiency in athletics isn't even a detriment when facing grapplers but for a handful of oddly worded monster statblocks.
Compare with the negatives of dumping dexterity - thus, strength sword and board builds are "bad" because they are inherently worse at all the many things a dex build allows and no better at others.
The best thing going for a strength build is (possibly) early AC, but soon enough even that one point of advantage doesn't matter so much (and at early levels, getting that suit of plate is damn expensive).
I think making dexterity a viable route is a good thing - but they've made it the
best option in most cases.