This might have already been mentioned but I will suggest it anyway. It would be really great if there was a way to do missions in the background. Some sort of an ‘away mission’ system.
To start the missions you still require the same energy and you still need the heroes at a decent level for the mission you select. Once those are locked in you send them off and wait 10, 20, 30 mins what ever time limit. This time limit could also increase the further through the story you decide to do. You then can select another set of heroes to farm another sector/stage.
You could also limit it such that you can only do one section at a time and any one hero can only be sent on one mission. Annnnd. You can only do this for stages you have completed with 3*.
Chance of failure would be base don the power/composition of your heroes you send and basically would have the same result if you just sent your guys off and left it on auto play.
The rewards are exactly the same as if you played through the stage or used quick win tickets.
I think this would be great for those that do not have a ton of quick win tickets but do have moments - like during the current bounty and blitz event - where they have more stamina than they no what to do with (I do not have this issue personally - currently have way more quick win than I can use).
To make it more appealing to the people that do have truckloads of quick-win tickets you could throw in extra incentives. Low percent chance of 1 fragment/gold or what ever, regardless of f2p p2p status.