We still do teach the difference between can and may.

Well, you're too late. We are not taught English if we are native speakers. We learn it, some say re-invent it, long before we get into a situation where we are learning it from any formal teachers. Some are capable of relearning, some appear not to be, when they find themselves in the formal learning situation. Some learn both versions of the language and use the one in normal situations and the other in formal situations. If the parents used can and may properly when the child is in those important years between about 0 and 4 when the glory that is language is forming whole out of Zeus' brow then there would be no need for the teachers to pound the "correct" form into the 5 and on up year olds' brains.