I am running CC applications using my personal account on my Mac (Mac OS Monterey) and on Windows (Win 11). I occasionally need to run Acrobat Pro on those machines using my business (academic) account. It seems that it is not possible to do that without a lot of effort. As I understand it, I would have to log out of all of my CC applications, then try to log into Acrobat with my other account, then reverse the process to go back to CC. No one in their right mind would want to do this regularly.

Adobe's login and licensing process is extremely onerous, and this is just one example. You should be able to associate a specific account with a specific application (or group of applications like CC) rather than one for everything on the machine.