My favourite asymmetrical style game was a last stand/city defence. Both players started with 2000pts, but every time the attacking army lost a unit it could be set back up at the start of the next turn. The game ended when the defenders were all dead. The defender scoring 1 campaign point for every turn they lasted.
When you brought up the old Generals Handbook I audibly went, “oh, that old book!” Looking over to my shelf. I always thought it was a nice open ended campaign system I’m glad to see it be even more accessible for any game system you want!