AFAICT, Apple excludes all their own apps. Seems like a way to try to get people to use Apple's apps over everyone else's. Just to check, I pick the Quick Time Player. I pick "New Screen Recording". No prompt.
But that's also you performing a positive action to start the (presumably time-limited) recording which is different from something in the background passively recording your screen over a long period (Bartender, etc.)
(I do not like the permission prompts but I understand where they're coming from)
If Apple wants to record your screen they don't need to use Quick Time Player to do it. They can bake it into the firmware.
If you don't trust Apple not to randomly record with Quick Time Player, you shouldn't be using macOS.