Bodily balance is part of mobility, climbing, jumping, and so on.
If Dexterity does almost everything, that in itself makes the other abilities more dumpable, thus effectively fewer.
Even so, in principle, Dexterity can deal more damage, such as by aiming more precisely with a bow. Certain weapons rely more on manual dexterity than on body swings, so I am ok with the concept of finesse weapons.
If the Heavy weapon property is instead a Strength prereq, then only Strength would access the higher damage weapons. Even a longbow might require a Strength prereq to draw its string properly, even if using the steady hand of Dexterity to aim it.
But the sense of balance should never have been split off into manual Dexterity.