Sounds like a nice idea

After all, the real pilots did keep their kill counts even when they were shot down.
This would naturally only affect the kill count, not points or perks. It would be fun for sake of kill streaks. Points and perks would still go along the current system. Stats should be updated to include the kill strek section.
Kills could be kept only when exiting on a friendly runway or hangar like nowadays.
The game system should be updated to allow picking up pilots and riding on others' vehicles or planes to make it work.