> I think C-u RET is probably fine, especially if we add a change like you
> described to compile-goto-error as well. But if anyone wanted to propose
> some other alternative, they're welcome to.

I want to propose another alternative: to implement C-u RET
not only for compilation-mode, but also for e.g. occur-mode,
maybe current-prefix-arg could be handled in 'next-error-found'
by adding to the end:

  (when (and current-prefix-arg from-buffer (not (eq from-buffer to-buffer)))
    (let ((window (get-buffer-window from-buffer)))
      (with-selected-window window
        (quit-restore-window window))))

But this means that it should take into account possible values
of the prefix arg of the command 'next-error':

  A prefix ARG specifies how many error messages to move;
  negative means move back to previous error messages.
  Just C-u as a prefix means reparse the error message buffer
  and start at the first error.

So since 'C-u M-g n' is already taken, an alternative is 'C-0 M-g n'.
If 'C-0' makes no sense for 'C-0 M-g n', it could be used to close the window.
Or maybe 'C-0 M-g n' still makes sense, e.g. to redisplay the current location?

BTW, here are the commands that work like TAB in grep-mode.
I propose to install this patch, so at least users could bind them
in own init files: