It can work that way, but it's also an uphill battle if you haven't reached your target body fat percentage. Building muscle is an anabolic activity, and losing fat is catabolic. It's possible to build muscle while losing fat, but it's hard because two opposed processes are fighting each other. For a really fat person, based on my personal experience, trying to build muscle while dropping weight isn't the best idea. Some people might be fine trying to lose body fat over a long period of time, but losing more fat initially and then building muscle seems less error prone than working out and then giving up after a while because the fat loss progress isn't encouraging enough.

Also, I would need to see some data that an average person is going to be able to build enough muscle while losing body fat to add on an extra 1000 calories to their RMR. I'm not saying you're wrong, but I'm skeptical based on my knowledge. In fact, I would pretty much say "no way" unless one can stay anabolic and dedicated enough to build an above average amount of muscle.

Have a look at this paper using your favorite hub of science.

doi:10.1097/00075197-200103000-00011

https://journals.lww.com/co-clinicalnutrition/Abstract/2001/...

Based on this, a pound of muscle has a REE ~6 kCal per day.

So to get to the number you are suggesting, a person would have to put on ~166 lbs of muscle. That's not realistic most people, let alone those with plenty of fat to lose. It also takes a lot of time and money (calories = cash).

A person could work out that muscle and burn more calories, but there's a few problems with this as a fat loss approach. For one, you're going to need a lot of glucose to have a meaningful workout so you're already undermining fat utilization. Second, it takes time to build up that kind of muscle. It's both a short and long term time suck.

Let's say an average-sized person puts on that amount of muscle and utilizes all of it during a 60 minute body building workout:

6 METS x 3.5 x 75kg ÷ 200 x 60 mins = 472.5 calories

While that's not anything to sneeze at, it hardly matters anyway because muscles don't burn fat. At best you're just preventing the wrong kind of weight gain. To even get to that amount of muscle and keep it on you still have to eat at least enough calories to match that anyway. This is why working out requires more working out, otherwise energy will eventually be stored in the form of fat.

Or, they could literally just not eat that 500 calories and spare themselves the sisyphean task of relentlessly working out and not losing substantial fat mass.

Some resistance training is a good thing no matter what, but expecting muscle to be a weight loss aid doesn't make sense to me. At best, it's an adjunct to fat loss and should be done in intervals.

I'm absolutely open to having my mind blown on this. :)