If armed, self-defense skills would include being able to quickly and efficiently access the weapon when moving, in contact with assailants or even on the ground and then be capable of being able to use and retain it under the same circumstances. Standalone unarmed skills as well as integrated with using the firearm are very important as well.
Being physically fit, strong and mobile is something that is infinitely useful in the context of self-defense as is deescalation and avoidance skills, an understanding of situational awareness(what to actually look for) and the tactics and strategies that actually apply to civilian self-defense.
Most armed civilian encounters that I'm aware of where shots are fired by the defender aren't actually entangled, but they are almost always at very close and there is frequently some contact(intentional or inadvertent) made. However, most people don't carry a gun, have no real training or skulls and are simply victims and there is also the possibility that some victims were carrying, but unable to access their weapon.
I can find pretty much endless video footage of multiple unarmed assailents(BLM, inner city kids, Antifa types etc.)attacking individuals, but hardly any where a gun was produced by the victims. If more people carried and had some basic close-quarter skills, I think the number of documented contact and entangled shootings would go up very dramatically. Keep in mind when looking at stats or available incidents, untrained people or those with average skills at best are generally involved, so a lot of what you see won't apply to a highly skilled, well trained individual. For example, what normally happens in most unarmed streetfight or bar fights wouldn't necessarily apply to the UFC heavyweight champion since his ability differs so greatly from the average individual. The same would apply to someone well trained in full spectrum self-defense skills.
When considering civilian self-defense in general, incidents do involve contact when you look at it as a whole including fistfights, physical assaults, rape, all contact weapon(knives, bludgeons), attacks. In terms of the attacker being armed with a gun, armed robbery, muggings, carjacking and rape are the most likely threats and they will occur at very close distances since the criminal wants something from you. Initial compliance or an unarmed response may be better than immediately going for your gun.
What I don't see with any regularity outside of two rival gangs engaging each other or miltary/police incidents is anything that resembles a protracted, ranged gunfight with two parties shooting it out with each other whether in the open or utilizing cover. Although exceedingly unlikely, if someone just started randomly shooting at me from distance in a parking lot or in the mall, I for sure am not going to stand there and draw my weapon and return fire. The most important ability would be the physical ability to move and extricate myself from the scene completely rather than engage. But, maybe your physically impaired and can't run very well. Well, luckily the odds of someone just randomly targeting you and shooting at you from long range or being involved in some type of active-shooter scenario is astronomically rare. So much so that I don't hardly give it much thought despite it being a popular topic on gun forums.
The bottom line is that if you're overweight, out of shape, have no training other than standing in a static stance shooting non-moving paper targets at the range, then I don't think you are very well prepared to defend yourself against the most likely threats you face no matter how accurately you are at putting rounds on target at the range. The only place I see traditional marksmanship possibly being of much benefit would be in certain home defense scenarios, but even then I think it a much better idea to avoid engaging at all or for as long as possible by putting as many barriers between you and the intruders to buy time with any eventual forced shooting subsequently being conducted at very short range. I also wouldn't rule out fleeing the home as the best response in some instances. If ambushed, then we're back to those close-quarter skills again.
Everyone has a finite amount of time, energy and resources, so it makes sense to me to allocate the majority of my training time toward preparing what's most likely. Pretty much everything is possible, but not everything is probable. And keep in mind, everyone has different abilities and limitations, so approaches will differ from person to person.