Do you have any specific ideas on how they could make them better?
If they are inclined on keeping mayhem (There is a certain addiction to the numbers flying off the screen) how about allowing you to choose different presets that challenge you to destroy the city in creative ways, and make it more engaging by making you think about how you will make enough to get gold. Perhaps allow you to choose a location to do it in, and if you get gold in all the presets, give you the option to customize the items your Character uses in it.
The Fight Club (or the idea behind it) would be nice to bring back. It was fun in 4, but a bit sloppy (they didn't seem to notice that the character pose at the beginning deforms your body horribly). The genki missions were fantastic, featuring some creative fighting scenarios. So, they could bring the best bits of Fight Club/Genki and wave mode (the phone calls are wave mode, so maybe add some actual people you need to help instead of invisible phone people) into a super fun thing that doesn't simply get boring. You could choose from arenas, genki courses, or city locales, and be given simple weapons at the start, and allow you to collect more and upgrade as you go through, via gifts or maybe some kind of exclusive friendly fire that only affects the mode (and vice versa) there could be boss battles in between, enemy variations, targets or things semi resembling the telekinesis ones in 4, balancing points and that super satisfying cash noise (I just love it for some reason). With allowing the player to modify aspects, and maybe an endless mode (or simply courses), maybe change aspects of the map.
It would be fantastic, and Volitions excellent writing and voice acting would have some time to go insane!
Its like, they could combine elements of activities to create much more dynamic situations, missions with flight or in the air could contain each others elements, have time limited enemies to take out (which are challenging or have a tactic to destroying them), things to catch in the air before they vanish, and variety simply depending on which aircraft (or mech, or super suit power or whatever) changes the position on how you fight. Perhaps you have to shoot items out in certain places for people to collect as well, it could constantly switch between different things (and actually not have the activity end in 1 minute with 3 to spare).
For whatever reason, I enjoyed the parkour activities in 4, perhaps they could add together more dynamically, you could run a track avoiding flames, then have to leap across platforms, then get on a bike obstacle course (or have to do tricks), then finish off with a retro tank boss battle!
Insurance fraud...hmm, I find it exceptionally easy now, I find myself flying into the air for minutes after the activities supposed to end. How do you add challenge to brutally injuring yourself... maybe simply hitting into cars just provides some points (even with air time which is so easy to accomplish), and challenge you to inflict suffering on yourself in bizarre and creative fashion (add some new hazards to the map, or if your car flying, challenge you to throw yourself targets or sections of buildings, maybe take a page out of GOOH with its awesome structures that have openings and ridges all across them, and challenge you to swing through them like barnstorming. (Imagine flying into an office building and fling across desks and cubicles!).
Few alright, those are improvement ideas based on already existing activities, but at the same time, it would be insane to accomplish all of this, and I don't know if budget or time will limit Volition (pleeeease take your time).