I think I agree with above that a system that simply rewards for play time or number of matches would probably have too much impact on the game style itself.
However, a daily job system that provides some more variety seems great. The idea is inspired by a shooter game but I think it would work here too.
1) Each day there is 1 easy task (takes like 15 min), 1 hard task takes like an hour, 1 multi-job ( 3 jobs one unlocks the next, summed up they take around an hour).
2) The rewards are appropriate for the task complexity eg. for 15 min job you get something small but useful like everstone(s?), braces etc. For big job or last job of the multijob I dont see anything bad in getting good cash or BP. I think that completing all jobs would take around 2-3 hrs and should give rewards worth 200-300k to be as effective as paydaying or npc runs
3) I think any sort of pvp activity that gives rewards should have some cheat detection system, so if your battles are super fast like 1 min or 2 or you afk before taking each turn they should not count towards daily job rewards.
4) Some ideas for PvP jobs:
- Play X matches in Y format (OU, UU, NU, Double etc.)
- Spend X min battling
- Win X battles in tournament mode
- KO X pokemon of a given type
- KO X pokemon using given type pokemon
You can make so many combinations from this so this would not get too repetitive and every day jobs would differ somehow.
Additional to this we could have rank system, you gain experience for the battles you play (more when you battle higher rank players) and upon reaching next rank you also get substantial cash reward.
I think this kind of stuff would really encourage people to actually battle and try to get better by choosing better opponents.