Hayden won his championship by default in 2006, by 7 points and because Rossi had 3 dnfs due to mechanical and tyre issues. Hayden only won 2 races Rossi won 5 and was clearly the better rider all year. To back up my suggestion, Hayden has won only 3 races in 11 seasons of motogp racing, and none since his championship by default!
He has always been over rated - IN MY OPINION.
I don't think as poorly of Hayden as you do, but I agree with several points. I remember the year he won the championship as pretty unspectacular. Yes, he was taken out by Pedrosa in one race, but as you pointed out clearly, Rossi had a bunch more DNFs, and Rossi's crash at that last race was pretty silly - handing the championship to Hayden. Almost suspicious...
I watched Hayden come up through the AMA series and he clearly was head and shoulders above the field. Not that that is saying much in the perspective of World's Best Riders, but he was the best we had to send over in a long time.
He did very well in the dawn of MotoGP, with 1,000 cc four strokes and no TC, his dirt background suited this well. IMHO, he simply wasn't able to adapt to the TC era and the traditional 250 2-stroke style of high corner speed vs. the SBK-style of get-it-stopped-square-it-off-light-it-up-exit.
This is why Rossi for me will always be the GOAT (greatest of all time). He won 125cc, 250cc, 500cc 2-strokes, then the first MotoGP 4-stroke championship, and continued winning, even through the TC era. Ago has more wins but he never had so much changing technology and riding styles to adapt to.
All that said I think Hayden's heart belongs in MotoGP and the only real option for him is Suzuki. From what I've observed, he won't pull an Edwards and go to CRTs or a Satellite team as it's not worth it to him at this stage in his career. Supposedly he is very well invested and could comfortably retire, but as he said in his Laguna press conference, he's not ready to hang up the leathers just yet.