"Can you?"

In elementary school, I was taught to say "May I go to the restroom?" instead of "Can I go to the restroom?" "Can I go to the restroom?" makes no sense, I was told, because I obviously have the ability to go to the restroom.

I have since learned that this "rule" regarding "can" vs. "may" is a mere prescriptivist nitpick. Prescriptivist nitpick or not, it raises a question.

We say "Can you open the window?" even though it's obvious that the person we're talking to has the ability to open the window. By contrast, it would sound odd to say "May you open the window" (unless we were wishing someone success in opening the window).

If we say "May I?" when making a request, then why don't we say "May you?" when making a request? Does English work that way just because that's how people talk, or is there an underlying logic behind it?