I want to be able to improve, but the current strategy in competitive is to bunch up, pick off one enemy player and then spawn trap the enemy team and team shoot them, because the group with more players shooting always wins since they can revive each other. Unless the people teamshooting break their crossfire and get picked off, the match outcome cannot be changed.
Ideally, the 1v1 game mode would remove radar entirely, lock loadouts and recharge abilities only with damage dealt, no supers. It would use the special ammo crate system with spawns only in the middle of the map to discourage camping, give one kill worth of ammo, and no heavy ammo. It would be round-based, first to three. To break the tie, damage dealt is considered instead of a zone, and health is lowered in overtime until both players are one-shot.
And most importantly, it should use very strict skill/rank based matchmaking. The tried-and-true strategy for improvement is progressive overload. CBMM will just push lower-skill players away from the mode until only the sweatiest of sweats are left (see Rumble).
If the concern is that there won't be enough players, bots with adjustable difficulty could be used to fill in the gap. There's another post that goes more in depth on that topic.