Now an important question is how one could rein in such signalling arms races.

Who or what is that "one"?

That's not an idle question. If you assume, for the purpose of this exercise, that the One is an omnipotent dictator then the signaling issue in education is a silly place to start molding the reality. And if you assume the context of a modern Western society where you can't just magically tinker with people's minds and motivations, then the first question is what capabilities do you have to affect the issue.

For comparison, consider the signaling games around the selection of a mate. Are they "socially wasteful"? Would you like to "rein in" these games?