I'm not sure it's a great idea. I like having my browsing history available and synced between devices. Also, if all private tabs share the same profile, it might be kinda pointless
It's actually something I adapted to and really came to like about using Firefox Focus (and have missed since switching to Firefox Preview). The main thing about Firefox Focus is it was extremely easy to reopen a page in a different browser or app (Chrome, Firefox, whatever). So some app on your phone would send you somewhere in Focus and you would peek at a website and then decide to transfer to the "real" browser if you actually cared.
I'm not sure it's a great idea. I like having my browsing history available and synced between devices. Also, if all private tabs share the same profile, it might be kinda pointless