Your preference for mobile site redirection is stored in a cookie and that cookie currently only works on the domain its set. It should be possible to set the preference across a project (e.g. switching language would honor the preference) but it's not feasible to do this for all projects.

Given it's feasible a user may want desktop on certain sites and mobile on other sites, assuming one catch all preference is unwise.

I never use the mobile view.

Millions (billions?) of people do.

Sure. I meant you do not need to check every time in cookies - it will be always the same.