I had this question myself and your post had stimulated me to finally research how to do it.
Here's the current solution (or rather a fix, because this behavior of the *Ido Completions* buffer looks like a bug to me) tested on
(window-height . fit-window-to-buffer))))
Additionally, try out
(setq completions-format 'one-column) ; or 'vertical / 'horizontal
Documentation on display-buffer-alist.
I probably should have also mentioned that typing
C-x C-f calling
ido-find-file) allows to fallback to non-ido
find-file with the currently more standard completions buffer behavior.
C-h f ido-magic-forward-char lists all
C-f initiated "magic actions".