Games like that exist.
I'm not sure how it is out in Alberta, but we've got them to varying degrees in southern Ontario. A lot of it is in the WWII reenactment groups, but they exist for "modern" or unspecified military eras as well.
You occasionally hear people (mostly Brian McIlmoyle) talk about how the most fun they've had are at games where they never fired a shot. Or where there's an intense pressure of "don't get shot, because you'll be out for the entire game".
After finally participating in such a game (~32 hours of trekking through an undeveloped forest, avoiding the enemy because we don't want to get shot out of the game, spending hours crawling slowly through a field or sitting around waiting or standing guard, and never firing a single shot for the entire OP), I can say that it is indeed very miserable and satisfying...And in retrospect, fun!
If you can make it out to Ontario in October for a Deadfall event, you definitely should!