I don't know what's up with your game, but you could try toggling that setting back/forth and checking it both ways to ensure that it's actually on that setting; I can tell that it's not because it's not using the Remote View, and it's in general behaving exactly like the Full Isolation setting. I don't know how you got into that state.
Okay, thanks to your info i figured out what causes my bug, https://mods.factorio.com/mod/no-remote-view-border I'm using the mod that removes the remote view border and turning it off and on fixed the issue. Thanks for the remote view mention!
Wait no, I was wrong, No Border mod had nothing to do with this. Entering and exiting BPS does not reset the remote link if you're sitting inside the spidertron but if you're outside at the time of entering/exiting BPS the link gets reset.
Here's a test on a completely fresh factorio install with no mods at all, the bug is present there:
I see that it sometimes works but not always. It appears to be a bug in Factorio, specifically around setting the Controller back to the Character via LUA. That must happen, so there's nothing I can do about it here, and a bug report should be filed with the Factorio devs. I found that if you're exiting the Sandbox via the shortcut/toggle with the Remote in your cursor, it doesn't happen. Better than that, exiting the Sandbox by closing the Remote View by its button, Escape, or the map shortcut, it also doesn't happen.
You're right, exiting via just closing the Remote View works.
Could perhaps a different keybind for exiting BPS be added, so you had an option of not being able to exit the same way you entered (and had to go through exiting remote view)? It'd be completely optional to bind different keys onto entering and exiting.