To be honest...it's because strength was considered the 'norm' for melee attacks since the earliest days of role-playing. No other really good reason. There are definitely weapons that could be better served by using Dex/Quickness/Reflexes/etc instead but to make things as simple as possible, most games have kept it to strength. Some games get around it by failing to offer any sort of armor proteciton against certain items (like the stun baton) but I don't believe SR does that (though I'm not positive).
Another related question to that is: Why not strength when dealing with certain aspects of firearms? Recoil is a big issue in real firearms. Really, what comes to mind is the video I saw of the cute, dainty little chick popping off a single shot with a Desert Eagle .50....and then watching as the recoil and her lack of upper body strength slung that DE .50 into her forehead. Proper stance, technique, and readiness can mitigate many of the effects of recoil...but not all. Sometimes it just takes a bit of the old brute force to handle it.
Was contemplating adapting a weapon min str system like CP2020 has. If I can figure the math out properly, the system would be almost intuitive in figuring whether that weapon is just too much for you or not.