Only if you don't want to use Steam. I'm not really sure what point you think you're making here by constantly asking whether you can use SteamOS without logging in to Steam. You can however install literally anything you like on a Steam Deck.

It's nice on something like Steam Frame where it's hard to install a new OS. Forcing a log-in like Windows is evil and sucks when you don't have internet.

Nobody knows if it will be hard to install another OS on the Frame.

The hard part is making one work on it since none already exist like the hundreds that exist for normal computers like Deck. They might not let their 6dof headset tracking code be shared and getting that working would be very hard.

Given Valve's past history in this regard I'm inclined to believe it'll be possible to install whatever you like on the thing, and that there'll be a reasonably well documented way of integrating with the sensors/display. Valve have got decades of form on being as open as possible with their hardware and I've seen nothing recently to make me think that's changed.

Software wise their SteamVR / OpenVR stuff is very closed source. Someone had to reverse engineer their Lighthouse tracking which is hard but doing that is easier than making 6dof SLAM tracking just from camera access. All I am saying is its not easy and people will have to do hard work.

Yes, they are Arch and Fedora Atomic variants respectively and don't require any accounts or corporate affiliation.

Yes you can use SteamOS without logging into Steam too!