I think they are much closer to the stereotype than they think they are; and certainly not so self aware as some might suggest.
They strike me as a trio who began identifying as journalists and now find themselves identifying as comic presenters, and at least one of them (clue here, he is a tall chap) seems to consider himself a comedy treasure.
May is the one that has the legs as far as I am concerned. Clarkson can produce great and informative programs, but the spectre of his lesser persona is never far from the surface.
I just wish they would drop the 'yes, we know we are being idiots and saying reactionary things to parody our public image' mockery, and move on in some way.
The world of motoring and transport, technology is diverse and fascinating enough to support a regular hour long programme, without resorting to overriding all the factual, journalistic elements in favour of indulging the egos and comic aspirations of three rather silly chaps who really should remember they are journalists/presenters with a sense of humour rather than humorists moonlighting as journalists/presenters.
Ipso facto, they just ain't funny.