Allow me to try to convince you.
A great deal of these “quests” could be part of that daily/weekly gameplay. As an example, my proposal for Zurg (see above) requires you to do 10,000,000 damage cumulatively with his Ion Blaster skill. If you have his Red Skill quest unlocked, he’s clearly a hero you’ve put time and effort into, so he’s going to be usable. Now all that needs to be done, is using Zurg in the eligible modes (Invasion, City Watch and Surge in this example) and activating his white skill. The damage from each battle is added to the total, and once it reaches 10 million (1 day, 1 week, 6 months, it’s up to how often you use him) that quest branch is completed.
If the red skill is something you want to focus on, you can knock out 10 million damage in the first few hours of Invasion with Zurg on a Blue week. In this way, some of these quests could be completed in the background while you do everything else, some could be completed while completing other quests, some could be your primary focus, but the main idea is that they have some individuality to them.