One way to breathe a new life into multiplayer shooters could be removing any guns from healers.

Make them potent, but vulnerable!

Why is it important:

• Players that don't like shooting, but love teamwork would finally be represented (yes, I'm speaking of your girlfriend!)
• Having to protect healers would benefit more organized teams, rewarding teamwork
• Healers would have a more dynamic gameplay revolving around avoiding damage: stealthy movement, ability to quickly traverse dangerous zones, coordination with fellow teammates are all required to benefit your team as a healer

What might need to be tweaked:

• Healers should be made into the only revivors, and we should either punish death more (which we'd better be careful of if that's a dynamic game) or give buffs on revival
• Healers should get more movement abilities to increase survivability. They may also get speed boost when running towards teammates (similar to Conduit Savior's Speed in Apex Legends)
• Team compositions should accommodate for several healers as to not introduce a single point of failure

Overall, I think it could introduce a new dynamic to team arenas and skirmishes, as winning now requires more coordination within a team and better understanding of everyone's roles.