I and many of my clients use membership sites as websites, the sites might have courses as well, but not all of them.
To me and my clients having the "Switch to the new experience" option visible for logged in visitors is really not what we want in most cases. Often it's pages with a carefully designed structure and menu, that is messed up with the vertical navigation. Or we simply don't want to confuse our users with two sets of interfaces, and we don't want to use the new one until it's more mature.
So what I'm suggesting is that there's a toggle to force the "new experience" off, just as it can be forced on.