If the ball comes loose after making a catch, it is already a fumble.
Yes, a LEGAL catch. Not just a possession + 2 feet catch which is what you're proposing for a legal catch. The receiver needs to either maintain possession to the ground or establish himself as a runner before he can fumble.
You're changing that completely with your definition and again, not allowing for a time element of a catch. A receiver can catch a pass with both feet on the ground, possess the ball for a tenth of a second, get blasted by a defender and the ball is jarred loose to the ground.
It's well-known that's an incomplete pass.
Under your definition, it's a catch and fumble.