Should I set my calories to 10 times my weight to lose fat?

For example, if I weigh 200, then that would imply 2,000 calories.

So what you're trying to tell me is that if I am 200 pounds and 8% body fat, or with 184 pounds of lean mass, I need 2,000 calories. You're also trying to tell me that if I am 200 pounds and 24% body fat that I need 2,000 calories. Huh? 152 pounds of lean mass and 184 pounds of lean mass both need the same calories to cut, even though it is estimated that a pound of muscle burns up to 50 more calories per day at rest?

Then I understand the whole, “well if you're cutting, this, or that.”

However, riddle me this ...

I'm 200 pounds 24% body fat doing the 10x rule. For my workout, I do 3 days of weight training for 45 minutes and 3 days of HIIT cardio for 20 minutes. 2,000 calories, right?

Now I have someone else who is doing Max-OT 5 days out of the week. They are also doing 45 minutes of low intensity cardio 6 days out of the week. So we are going from 2.5 hours of weight training and 1 hour of HIIT cardio to 5 hours of weight training and 4.5 hours of moderate cardio, and we still need ... 2,000 calories?

Just making a point. I don't think the x times body weight rule is good for much more than a wild guess at where to start. Ultimately, you should be consistent and adjust your intake based on your actual results.