Double counting the notice period is unfair IMO. You already pay for the notice period by having the notice period when you want to quit. Companies having to pay you the notice period when they fire you is symmetrical and IMO is not a severance package. Maybe that's just my assumption, but IMO a severance package is the asymmetrical pay-out when one party quits an agreement, not the communal wager you both put down when you enter the contract.

Put another way: if both parties agree on a shorter or longer notice period, I wouldn't expect that to affect any potential severance package. It's just the notice period.