It's about controlling relatively large amounts of mass for several minutes at a time, with your arm partially or fully extended. One arrow weighs about 1/40th the weight of a sword or other large-ish melee weapon and despite the high pull of a good Welsh bow, you only need control it for a few seconds.
Dexterity matters, sure, but arm strength keeps that weapon elevated. The fine motor control won't matter if your gross movements aren't up to the task of getting the weapon into proper position.
Hell, you see that with boxers: the longer heavyweight matches, it's not a lack of dexterity preventing them from keeping their 16oz gloves elevated, it's that their strength is sapped.
I disagree. In game terms, it isn't that the boxers have lost strength, but rather the constitution to utilize that strength. Endurance is a factor of Con, after all. A hypothetical boxer with superhuman constitution shouldn't have any difficulty keeping his gloves elevated, IMO.
As someone who has studied the martial arts, I see where Siberys is coming from. Strong guys are hard to block (because despite blocking, the impact still goes through you), but at least if you can avoid their attacks they're not that bad. In my experience it's the tall, thin, fast ones that are the hardest to fight. It doesn't really hurt to block them, but with their reach and speed they're very hard to avoid or block at all. That's in regard to unarmed combat, of course.
When using weapons, I agree that strength does play a role, but to what degree depends largely on the weapon in question. A dagger doesn't require much strength to wield. Nunchaku are completely dexterity based. On the other hand, I'd say that a staff leverages both strength and dexterity in roughly equal proportions, while I expect that a Claymore relies almost entirely on one's strength.
Moreover, as with the boxers, constitution plays an important role. It doesn't matter how strong or dexterous you are if 20 seconds into the fight your muscles cease responding due to fatigue. You also have to take into account that outwitting an opponent (Intelligence), leveraging your environment (Wisdom), and even self-confidence (Charisma) can be significant factors in a fight.
Saying that Strength is the only important factor in melee combat is a vast oversimplification.