Switch to last window

Question

I am trying to use the code from this answer: Is there a generic toggle-previous-window function?

(defun switch-to-last-window ()
  (interactive)
  (let ((win (get-mru-window t t t)))
    (unless win (error "Last window not found."))
    (let ((frame (window-frame win)))
      (raise-frame frame)
      (select-frame frame)
      (select-window win))))

I had to add: (select-frame-set-input-focus frame) to make it work. But with this code or just switching windows using the mouse I have the following problem. Imagine I have two frames, one with one window f1_w1 and the other with two windows f2_w1 and f2_w2. When I switch from f1_w1 to f2_w1 there is no problem, but when on the next cycle after f2_w1 -> f1_w1 I switch from f1_w1 to f2_w2 I can see the cursor first appear on f2_w1 and then quickly jump to f2_w2 making my last visited window f2_w1 and not f1_w1 as it should be.

EDIT: as per Drew's comment below that asks for the question. I just find it surprising that Emacs can't properly track the last selected window (unless something is messed up in my configuration). It seems that get-mru-window works as expected but switching to a window on another frame seems to be a two step operation under the bonnet, where Emacs selects the previously active window on the target frame (not the one I am switching to) and then quickly jumps to the one I am selecting. Is this behaviour unavoidable when using multiple frames?