I don't really like that. The monk already cares about two stats why give them a feature that only works if they bump a third?
1) A 12 under most systems is cheap, and it grants a +1 to damage.
2) It opens up a new monk build; a strength/dex monk that focuses on damage.
3) As it stands, strength is less useful for monks than most other combatants. So investing in it is sub-optimal. And the fact that martial artists are all weaklings feels bad to me.

By adding strength+dex to monk unarmed damage, I bump monk damage by a few points under a "typical" monk build "for free". And I encourage monks that aren't physically weak.

To me, there is nothing wrong with a class having a use for 3, 4 or 5 of the attributes. You just (a) don't assume they are high (I assume a 12 or 14 strength) for how much they boost, (b) have to make sure if they are high it doesn't break things.

A Tortle 16/16 monk under "add both" deals 1d4+6 damage with a punch, times 2, at level 1. That is strong, but not game breaking.