Nobody's denying that the "singular they" went out of fashion due to a prescriptivist rule. Mike's point is that the fact that it was acceptable in Shakespeare's time does not, in itself, mean that it is acceptable today.
The fact is that, rightly or wrongly, most people today find the "singular they" unnatural and odd. That's not because they're deliberately following some prescriptive rule, it's because that's the way they've always used the language. You suggest that students have to have the "singular they" actively drummed out of their heads, but that's simply not the case; few people write or speak that way in the early 21st century, and that's a fact.