Interesting topic. Here's my two cents. First, I have competed for years in IDPA,.Steel and now USPSA. They are not training but various skills practice. I find good and bad points in each as regarded for EDC. That's a long discussion for many over the years and rant fest for truth believers.
Jeff mentioned the NTI. Did it three times and had very high quality FOF and simujlated well scripted incidents. It is orders of magnitude different from a match. Fast draw shooting skills are a small part of it. All the participants had those. You can get hurt and look like a fool. Folks there stressed out and flash backed - had to be talked down, told to breathe after a run. Police, military, professional instructors, high level zealots (moi). For example, a Marine colonel in charge of their marksmanship training, IIRC. Serious folks. The solutions weren't always the guns, might be avoidance, talk, etc. Dealing with the law after the 'shooting'. The whole package - not what you find in a match.
Be in a terrorist attack, without a gun, disarm an opponent, shoot said opponent, be standing with the gun when the law floods in.
Did a fair amount of other FOF at a high level. It is good for stress inoculation - you don't freeze up, you do things. Did see folks freeze.
As far as doing push ups and running, that is all well and good. However, now at my age - it is not happening. Serious training gives you a mindset and paradigm for an incident. It has served me well.
If you are serious, a good FOF experience is an eye opener. For someone who wasn't in the military, it was worth my time.