It's not a bother and I encourage these types of posts. I try my best to read everything since it helps me brainstorm more stuff.
I had a similar idea also where p1 and p2 take turns on rounds and try to score more points than the other person. The kick for this one is that the player not currently playing would be a flying thing (idk a ghost or machine thing) and can shoot, spawn enemies, or drop traps that might mess up the player currently playing.
I do like your idea also and I might experiment with both to see which clicks more.
Thanks for playing! :)