Proposal: let people complete missions faster with specific icons on...
...but also allow people to complete them without those icons. For example, something like 50% bonus progress with icons. If you have to kill 120 enemy champions as a team, it would mean people can either use the icons and kill 80 champions, or not use the icons and kill 120 champions. People will feel good about using the icons that way.
Doesn't have to be 50% if that seems too big. It can be anything. The main idea is to give additional bonus to mission progress (but not reward) by using specific icons.