Scars Unseen
Hero
I think when you get to the point where you have to edit the entire equipment table to justify changing the way a single rule is applied, you've either hit the point where the justification for your house rule is thin to the point of translucency or that you need to reassess what it is you want from weapons and just house rule the whole thing.I mean the keyword could be anything else, here it's just repurposing a keyword that has an understood meaning.
You could simply see the house rule as making ALL weapon STR-based and Finesse being for exceptions, which includes bows.
Crossbow would then be moved to the special cases like the net.
Frankly, I don't see the justification for the house rule as offered beyond "I want." If we're talking about how strength might apply to bows, I can certainly see an argument being made for damage assuming one were using a bow with heavier draw than normal, but even if one were to apply similar logic to the attack role, I don't see an argument that would convince me that a bow could be just as accurately aimed by someone with low dex as high.
If the goal was "what can I change that let's strength focused characters take the bow as a valid choice," I'd probably offer the following: first, add a weapon property called "strong pull" that allows the character to add either their dex or str to their damage roll, whichever is higher. Second, I'd add to the feat "sharpshooter" the following: "when using a bow with the 'strong pull' property, the character adds their strength modifier to the attack roll in addition to their dex modifier."
It gives a clear benefit, requires some player investment (but gives even more benefit in return), and doesn't make things confusing by ignoring the meaning of words as well as the obvious intent behind them.