But he isn't very popular anywhere else either, certainly not with the government, which turned down his finance submission and now finds itself accused by even the right-wing papers of destroying the Beeb.
And, of course, the thought of a reduced Beeb makes everyone think.
We may have a pretty vibrant market in the UK in terms of new media options, but they're all chasing a more or less finite pool of advertising so they're hardly likely to spend buckets on "important" programmes.
ITV has lost its monopoly so we won't be seeing a new 'World at War' from them any time soon.
Not that the BBC is making these shows either. Now that Simon Schama's big series on the history of Britain has run out, digital channel BBC History is reduced to running re-runs of 'Sharpe', bits of old David Attenborough (hardly history) and even 'The Antiques Roadshow'.
C'mon chaps, are you taking the piss, or what?
Then we have the BBC's still more or less independent news output. John Humphrys on 'Today' and Peter Allen on Radio 5 Live still give government ministers a hard time. As, of course, does Paxo.
But a reduced BBC would reduce this ability. You don't have to talk to Sky or ITN or 'Channel 4 News'. But if you duck 'Today', the thinking classes think you've got something to hide.
But 'Today' is increasingly filled with flim-flam from single issue pressure groups and academics bringing out daft reports on something or other to justify their existence.
There isn't actually that much news on the programme these days. Why? Not enough reporters, perhaps?
But Thompson is cutting news jobs.
Yes, we all know the Beeb doubles up (or triples) too much on some jobs and there is a case to be made for an "integrated" multi-platform newsroom (aka The Telegraph).
But this is a matter for common sense and better organisation (and fewer bureaucrats).
If you get people running around like blue-arsed flies serving the needs of various "platforms", you're not going to get the kind of thinking and preparation time that make for good reporting.
Thompson, of all people, should know this.
Just today, the Beeb has announced that it's going to take ads on BBC.com (its international website). Actually, it should take ads on its UK-based websites too.
Very sensible anyway, but knowing them they'll hire 70-odd minders to make sure they're not doing anything they shouldn't.
So another good idea will head down the tubes.
The BBC needs to be smaller, or at least not cost us licence fee payers any more money.
With an income somewhere north of £3bn this ought to be achievable.
Arguably it should have an editor-in-chief, a CEO who knows what he or she is doing and the ultimate governance should be handed to Ofcom rather than the inept Trust that does it at the moment.
And Thompson should go.