The main goals would be thus:
Add another negative to dumping strength.
Add an incentive for ranged attackers to raise strength as well as Dexterity.
Of course, Crossbow Expert would need changing to not totally negate that last point.
So without knowing what the change to crossbow expert is, we got no foundation. Ok.
So, ignoring the crossbows entirely then and only looking at bows...
For the subset that have longbows extra attacks and 8 str, those builds vanish... they go away... gone... replaced by builds with short bows and 10 str and 2 less on some other fourth down stat. The penalty is not so much a penalty as making that subset of builds no longer worth even looking at.
So, favorite picked, offending choice being used now de-facto banned cuz nobody with an 8 str multi-shot longbow is gonna drag 5 ability points from elsewhere to keep that when shortbow is almost as good for just 2 pts drag. (Side benefit - gets their weight carried a little more buffer room. Maybe an armor up-tick.)
For the sub-set of longbow using 8 str guys who rely on one shot anyway (rogues delivering sneak maybe) they keep their 8 strength and elven longbows no prob. They did not have more than one bow shot before so loading is irrelevant.
So, is this a success? It drives out dex-based warriors with longbows driving them to shortbows and it lets longbows be the dex weapon of the rogue-based builds (elven weapons for instance)
So, is that success as far as bows is concerned? More warrior shortbowmen and more rogue longbowmen? If so, great - Mission Accomplished.
But if you wanted to make a 13 str vsc8 str longbow dex-heavy fighter a viable trade-off option - make these "tough choices" as to which to choose - nope. You just made that a trap.
5 ability points drag-in to get longbow vs 2 ability drag-in for shortbow is not gonna be measured and found balanced by most anybody. Especially not when sharpshooter eliminates the range penalty so we are seeing 320 ft vs 600 ft as so rarely a factor.
So, the "penalty" really doesn't get played... just one subset abandoned and shifted to different builds.
What if instead, you start everyone at 10 strength? Then you get rid of dump stat bow builds pretty cleanly.
Maybe you let them choose baseline between
Your three physicals are 10 and mental 8.
Your three mental are 10 and your physicals 8.
That way, you eliminated martials dumping strength but leave 8s for the brainy guys.
We can talk crossbows once we have the new cross expert.