A Question re: Strength

If one uses, as OD&D, AD&D, and Empire of the Petal Throne do, a one-minute combat round, I think you're committing yourself to a broadly abstract approach to combat. As Gary Gygax explains in the Dungeon Masters Guide: "During a one-minute melee round many attacks are made, but some are mere feints, while some are blocked or parried." 

If one understands combat in this way, I think it makes sense to avoid talking about "to hit" rolls, since, over the course of the round, there may be many attacks, some of them even landing a blow on an opponent. Rather, the combat roll determines whether or not any of those landed blows are strong enough to overcome the opponent's armor and deal damage. Thus, the "to hit" roll is really more like a "to damage" roll.

Consider how common it once was – and perhaps still is, for all I know – to criticize the way D&D uses armor class. Why, I recall being asked, does wearing plate mail make a character harder to hit than if he were wearing chainmail or leather armor? The answer is that it doesn't. Rather, certain types of armor make a character harder to damage, which is why I recommend dropping the use of phrases like "roll to hit" and the like.

All of this brings me to my question about Strength. Prior to Supplement I, a high Strength score conferred no mechanical benefits beyond a bonus to earned experience for fighting men. With the publication of Greyhawk, this changed. Now, a high Strength granted a bonus to "hit probability" and to damage. Given the understanding of the combat roll I propose above, does it make any sense for a high Strength score to do both? 

A bonus to the chance to deal damage (called "hit probability") makes sense to me, since what that really indicates is an increase in the likelihood that a character can land a hit solid enough to harm his opponent. I find it reasonable that a high Strength might assist in this. Why, then, a bonus to damage dealt as well? Isn't that "doubling up" on the Strength's role in combat or am I overthinking this, as I often do?

I hope I've explained myself clearly enough so that my question is intelligible. If not, I'll do my best to clarify my position in the comments.