I think the question is largely moot until there are vaccines actually going to waste, and for the most part that's not happening yet.

If there are tiers, then teachers should be in one of the earliest tiers. If there aren't tiers, then doses should be reserved for teachers, health-care workers, etc.

I haven't fully followed the argument on whether tiers are good or bad. I imagine the issue is that the existence of the tiers introduces unnecessary complications and slows the process down more than they streamline it.

For example, mathematicians have studied the most efficient method to board passengers on airplanes. Should passengers be boarded in many small groups or in few large groups? Should the groups be defined by rows? Front to back, back to front, or something else? Or should they be defined from outside to inside (window, middle, aisle)? It turns out, if I remember the paper right, the one simple strategy that's more efficient than any of these strategies (including the standard airline strategy) is to board at random. Let the people on the plane in whatever order they got in line. Basically doing it randomly will naturally minimize conflicts of one person blocking another, at least to the extent that these conflicts can be minimized. The problem of boarding a plane is not the same as the problem of vaccinating a population, but I imagine a somewhat similar argument could be made for vaccinations, though I'm not sure.

At any rate, as I said above, so far the number of doses wasted because the right kind of people can't be found at the right time, seems to be minimal. So I'd probably say if it ain't broke, don't fix it.