I'd like a few things.
1) Keep the focus on cooperative play
2) Make the overarching story more important. (more like the adventure card games), establish a sort of loot system. You start a campaign and add to your deck/collection by beating a mission.
2a) This allows for multiple win conditions with different cards added to your deck pool as a reward and lets people replay the same campaign but make different choices to establish a different path
3) Less auto-include cards
4) Personally I really like the way Conquest deck building works, not necessarily with the alignment wheel but something like an investigator who comes with 7-8 cards attached, then you build your deck around that investigators theme. I'd like this with something akin to net-runners influence theme,
I'll be playing both games if they exist.
To describe (2) a bit more. Maybe have a core set with all the cards and 3-4 mission. Each mission comes with 2-3 sets of reward cards that players add to their deck as they when they complete the mission. A similar scenario could be completed for packs. A new scenario is added to the campaign, once beaten you'll be able to add the cards to your deck building choices.