With regard to tyres, I read a really interesting article a few weeks back, where the journo asked Pirelli why they hadn't bothered trying to get the MotoGP contract.
Pirelli's man stated it's because MotoGP tyres have no relevance to road tyres
whatsoever.
He stated the most common pressure to run MotoGP tyres at is 9psi (

) and MotoGP tyres can actually run perfectly well with 0psi. (double

)
He stated Bridgestone will be learning nothing of relevance to road tyres from MotoGP and are doing it purely for the 'kudos' of being the title supplier.
Which is something Pirelli are not willing to do.