Of course you could always start a new campaign with the same squadron. But you will start all over with completely new AI comrades etc. So besides the squadron everything is completely new generated.
The point of the new feature is to continue where you left off with the same squadron and same squadronmates with all their names and stats, medals, injuries, aircraft complements etc. So if your pilot dies, you can re-enlist a new one (usually rather with a new name) and continue as a replacement of your former alter ego. So you can continue the story of the squadron and with the same ai mates you got used to.