The one part of the market where they will continue to see competition is for those payloads/trajectories where there is no way to land the booster.
Secondly, it's my understanding that with the performance upgrades from the Block 5 iteration that will become the dominant configuration later this year there will no longer be a need to fly the booster in expendable mode. And with the ability to launch much heavier payloads on the Falcon Heavy for extremely low prices, there won't be much of any performance window anywhere that competitors could wiggle through.