Nope. I don't like this idea at all.
First, I play the game because of the Star Wars theme. And part of that has always been that some characters have iconic ships. Han and Chewie fly the Millennium Falcon. Wampa doesn't fly Slave I. End of story.
Second, your idea will mean that—as already happens too much, in my opinion—only the top slice of our roster will get used. Everyone else will be useless. I like that characters that aren't meta themselves still get to contribute as pilots.
I agree that CG should revisit pilotless ships' stats to make sure that they're staying relevant as additional relic levels make piloted ships more powerful.
There are already plenty of characters in the game that are still waiting on their ships. I'm sure more will come as well.