Strength is better already, which is the problem. Moving shields to strength would make it more unbalanced.
Just so we get things straight, I don't care about the unbalance as far as game mechanics go. I care about it as far as diversity goes. A HUGE portion of the playerbase already stacks strength. This would cause even more people to do so, which in my opinion makes the game boring. The game would be a lot less fun if everyone was a roided up douche blindly swinging a poleaxe.
Definitely would be a lot less fun, but making shield difficulty based on strength would not have that effect. Here is what I think might happen:
Ranged chars would have to deal with more shields on the battlefield, BUT the shields they did face would break more quickly.
Throwers who use shields will be buffed because they can take points out of shield skill if they wish.
Hybrids who use shields will be buffed.
Crossbowmen and archers may start taking shields more often.
Two extremes of shields: Higher difficulty, heavy shields (board, huscarl, steel, etc.) that are slow, and because of their str difficulty, harder to max shield skill (Utility shields). Lower difficulty, light shields (cavalry, bucklers, etc.) that are fast and because of their low difficulty, easier to pair with shield skill (Duelist shields).
I wouldn't mind a buff to agi or WM along with this