Competition shooting definitely improves your shooting ability, if for no other reason than trigger time, reloading and weapon handling reps.
That's a valid point, I agree. A lotta folks who CCW for personal protection don't have near enough repetitive "trigger-time" to make it count on the street, i.e., in a real-world SD incident.
In the Martial Arts one gets better by practicing and sparring, combat shooting is no different.
That depends on which MA we're about, ... and more importantly, what you're training for.
If it's strictly fancy-prancy forms & kata dojo stuff, then it falls somewhere between irrelevant and useless on the street.
If you're talking instead about MMA-type training, that's different. MMA training imparts a "street-reality" to self-defense that's virtually identical to training for a real-world gunfight.