>>> If the M-: is not in a recursive minibuffer, everything is OK since 
>>> icomplete-simple-completing-p returns nil.
>>
>> Indeed; patch attached.  Ideally this should be done inside 
>> icomplete-minibuffer-setup, but if we did this (by checking 
>> minibuffer-completing-symbol), it would prevent icomplete-mode from 
>> being active in the opposite situation: M-: followed by C-x C-f.
>>
>> @@ -1754,7 +1754,9 @@ read--expression
>>            (set-syntax-table emacs-lisp-mode-syntax-table)
>>            (add-hook 'completion-at-point-functions
>>                      #'elisp-completion-at-point nil t)
>> -          (run-hooks 'eval-expression-minibuffer-setup-hook))
>> +          (run-hooks 'eval-expression-minibuffer-setup-hook)
>> +          ;; if we enter a recursive minibuffer, disable icomplete (bug#45474)
>> +          (setq-local icomplete-mode nil))
>
> Is this really specific only to read--expression? I can reproduce the 
> same issue with any command that doesn't use completion, e.g. C-x C-f 
> C-x f.
>

Indeed, but the bug report was only about read-expression.  It's far more 
annoying to see completion candidates when you want to type a complete 
expression than when you just have to enter a short argument.

Anyway, given that you asked for it, here's a more general solution.  I 
did not check all places where read-from-minibuffer is used, but adapting 
them is straightforward.