Anything related to saving and protecting people in a real-time action game, particularly for games that purport to be superhero experiences. Stuff like carrying civilians/bystanders to safety, telling people to get to safety, pushing them out of the way of danger, and so forth. For superhero games in particular, this seems yet to be fully realized.
I really enjoyed the Batman: Arkham series because they continually translated more combative Batman abilities from their source material into a fully playable form. Saving people was almost always a scripted deal though, not something that occurred in real-time.
This would be really difficult to make work, especially since escort missions are among the most notorious and frustrating in all video games. Having to worry about civilians while battling a supervillain in a public space could be compelling, but could also be a nightmare to build.
Would prefer it be proactive rather than reactive (e.g. the inFamous series has let players revive injured people after the fact, but that’s about it).