Pretty sure there isn't a "whole market just waiting for" Nerf Deathmatch.
Actually, there very probably is. Deathmatch without the completely-unnecassary-anyway blood splatters. Fun weapons that cover you in goo, or shrink you to a tiny size, or whatever. Stuff you can play with your kids without the whole simulated murder thing going on. And yes I know we should all be outside climbing trees and/or inside singing songs around the piano, but video games can be quite fun.
There are lots of Nerf Deathmatch games. One I remember in particular, was based on the Unreal 1 engine Nerf Arena Blast. It came out around the same time as UT so it felt very similar. There are plenty of gameplay videos on youtube.
I had fun with the demo back in the day