I think this is a bad idea, but if you want to try it and think it will be more fun, go ahead. I know I wouldn't play under that restriction.
The point system is already designed to limit the number of named pilots. And I actually disagree that this would hurt the rebel side more. For example, I won Kessel Run yesterday with a 4-ship Rebel build of only 1 named pilot (Wedge) in a 100 point squad. I built that squad hoping to be competitive, so I had to limit myself on named pilots in order to get that 4 ships in under the point limit. The Imperial builds I saw, on the other hand, all used 3, 4, or 5 named pilots. So I actually think they would be more limited than the Rebels. Especially from the point of view of variety of builds, which is a big part of the fun factor of the game. If you limit the number of named pilots, the number of viable squads is much smaller (especially in Wave 1),
Bottom line: not recommended. The game is already well designed and balanced without this proposed rule.
Be seeing you.