Not such a bad idea. After all, in real life, speed is related to Strength. The only problem is what is the point of Agility to a Warrior then? Strength affects damage, so if you had 100 Strength instead of 50 Strength and 50 Agility, you could hit twice as often and do twice as much damage. It's a little unfair.
But then, the same goes for Intelligence. It's near useless to almost anyone bar a Wizard. That's why I prefer Diablo II's combat system. Each attribrute is required by all classes.