I haven't been paying attention to MotoGP for a while, so I don't know how long the unedifying practice of changing bikes during the race has been in place. Doesn't really matter: it sucks big time, and takes away an important aspect where MotoGP scored over Formula One.
Maybe it's my belief in the KISS principle, but the idea of starting and finishing the race non-stop and relying only on your driving skills -- as opposed to the scheming and tactics associated with pit stops, fueling, tyre change, etc. -- appeals immensely to me. While we are at it, why not dispense with having two drivers and cars per team as well? It leads to charges of favoritism and ill feelings between the drivers, and results in violations of the spirit of racing when one driver is instructed to let his partner win in the interests of the team.
There is also a financial benefit to the no pit stops strategy -- think of all the money saved because you don't need such a large crew in every race.