Ref T8449. Try out some more subtle behaviors:

• Make the "Space" control part of the policy control, so the UI shows "Visible To: [Space][Policy]". I think this helps make the role of spaces more clear. It also makes them easier to implement.
• Don't show the default space in headers: instead, show nothing.
• If the user has access to only one space, pretend spaces don't exist (no edit controls, no header stuff).

This might be confusing, but I think most of the time it will all align fairly well with user expectation.

• Viewed a list of pastes (saw Space with non-default space, no space with default space, no space with user in only one space).
• Viewed a paste (saw Space with non-default space, saw no space with default space, saw no space with user in only one space).
• Edited spaces on objects (control as privileged user, no control as locked user).
• Created a new paste in a space (got space select as privileged user, no select as locked user).