I'm a big fan of ido-mode, so much so that I would like to use it for things like describe-function or find-tag and so on, without having to write something like in "Can I get ido-mode-style completion for searching tags in Emacs?" for each one.
Both
(defalias completing-read ido-completing-read)
and
(setf 'completing-read 'ido-completing-read)
don't work, at least partly because ido-completing-read calls completing-read in its body, so any simple redefinition would result in infinite recursion.
In theory, it should be possible, since the first line of the docstring for ido-completing-read is "Ido replacement for the built-in completing-read." I've looked around a bit and can't seem to find anyone else who has attempted or succeeded at it.
I realize that Icicles probably provides something like this, and I may end up going with that anyway, but it is a bit more of a plunge than I care to take right now.
Thanks for any help.
I don't think ido-mode is ready for this quite yet. In particular, ido-completing-read currently only works with strings, while completing-read supports alists as well. This is very important once you want to have a different user-level description of the items you want to complete on.
Therefore I am not surprised that it doesn't work out of the box, yet. Short of modifying the code yourself your best bet is probably to just file a bug report/feature request.