Is the TEF a solution that has finally found a problem?

Totally agree!!

Well yes I agree. I do remember when the fees policy was implemented that the fees were variable from £7.5k to £9k with the view that Universities which did not specialise in high cost, intensive laboratory and other Research would charge the lower end of the scale say £7.5k and the big Research intensive Universities ("prestigious" as you put it, but Russell Group in practice) would levy the max £9k. This would thus introduce a market into HE. Obviously, such a policy was prima facie utterly foolish as was proven very quickly ("Two Brains" indeed!), and almost all charged £9k irrespective of their rankings or prestige or their research intensity. But in this scenario, it was never assumed that you would get better teaching for your £9k, just obtain degree from a "better" Uni with more overheads, as it it were, and that Teaching Universities would be cheaper as they did not have expensive research establishment to fund (especially medicine). But in practice, students still preferred the "prestigious" places. So the alleged subsidy of R by T was always well-baked in to the equation from the start and, in theory, better-focused teaching should actually cost the student less at those institutions more focused on teaching without those pesky research overheads to fund. We also shoud be aware that when we talk about the erosion of the value of the original fee, originally the costed baseline for teashing was £7.5 and not £9k, so it's deterioration in real terms is not really as great as claimed. It was also always understood that AH subjects (which are or were then popular) would be used to cross subsidize the Teaching of more expensive laboratory subjects and the pay off for the student was in having the degree from the "prestigious" institution and the concomitant employability and cultural capital benefits?. I don't know if this is still the case in practice though and I am happy to be corrected. So we have to take this notion of Teaching subsidizing Research with a grain of salt in my view, and, as was rightly said, at University level it is the understood norm that research informs (or should) inform teaching and that students are taught by professional researchers, unless we are redefining Teaching in some more utilitarian, pragmatic way (which is a much cheaper option to fund of course!). We, of course, foolishily muddied the waters (in my view) by allowing profiled "Teaching" or "Education" cointracts with no research expertise or time built in (what some places refer to as "scholarship" as opposed to research). So to some extent we have only purselves to blame for this mess.