Although I was refraining myself from this matter because I'm completely new here and this is not my fight, like a say in my country: "Opinions are like underwear everybody got theirs". Here it goes.
There is no perfect rules, any championship with to strict or to soft rules will be a mess. I think rules should evolve with experience and especially around those who make the best of them (let's just say the senior drivers, drivers that make this championship happen and have been here for a while).
It's just like real life, how many times it happen someone wants something but nobody listen, then something happen to a major content (Gilles Villeneuve, Ayrton Senna, etc...) and everything changes. That's not fair all the way, but in the end the reason prevails.
I'm new here, but I don't see a reason why a different/better/more suitable car shouldn't be used by any championship rider but can be easily used by a newbie (just like me, I just choose the car because it was the only one that was unpaired, not even got a clue if it was the best that suited me or not).
For instance what prevents a rider from removing itself from the championship then applying again to a new car that is available. Things like this append all the time, in real or virtual life, it's not cheating, just playing hard by the rules and bending them to a result. But it's not pretty to see and if it can be avoided by tweaking the rules one way or the other then it should be.
Mid season team/driver changes occur at the top most racing championships on the world, so why not allow it here.
Why not half compromise, for instance allow one car change for any rider during a championship. Keeping in mind that the rule must always apply for everyone in their request order.
I'm a completely newbie here! I don't want to mess this up by any mean, this is a established championship. This should be read just what it is, a mere opinion.