Who's the real expert? The guy who's had all the "training" but has no actual experience, or an old farmer/construction worker/whatever who's had no formal training, but has actually done the stuff?...
Someone else will have to help here, but I would imagine that the training at places like Blackwater, Gunsite, Thunder Ranch, and the National Tactical Invitational are in fact based on real world experience, as are the Top Gun School for fighter pilots (founded by people who taught what they learned in actual combat), the Red Flag competitions, Marine sniper training, and so forth. Even engagement level simulation
has proved itself in military training.
The carpenter example is really not a very good one, in my opinion. You can find many skilled carpenters, but there aren't any fighter aces still in the saddle. That certainly doesn't mean that our best trained fighter pilots aren't "real experts."
They can tell you what tactics will get you killed nine times out of ten and what is likely to work. I worked for and with some Viet Nam era fighter pilots who could tell you the same thing, but they often knew that from training before they went into combat. They aren't flying anymore but they did survive. A carpenter can learn from trial and error, but a fighter pilot cannot.
The same thing applies in SWAT team training, to choose a more relevant example. Every so often the police teams do go into actual action against adversaries. If they based their tactics solely on those few events, with all of the variables involved, they would be at a significant disadvantage.
So, to become and remain "real experts", they train in realistic conditions, varying the scenarios until they are in fact real experts under a wide range of conditions. By the way, that's what fighter pilots do, also.
I wouldn't underestimate the value of professional, realistic force on force training and simulation. I have friend who is a police officer who has been in quite a bit of it. And I certainly would not adopt a strategy that the top professionals and instructors have found to entail a virtual certainty of getting "killed."
I hope this proves constructive.