>> Does Icicles support history completion in eshell and comint?
>
> Yes, I believe so.
>
> Command `icicle-comint-command':
>
>  Retrieve a previously used command.
>  Use this in a `comint-mode' buffer such as `*shell*' or
>  `*inferior-lisp*'.

It seems `icicle-comint-command' does the same as
`comint-dynamic-list-input-ring' bound to `C-c C-l'.

Maybe the same key `C-c C-l' could be bound by default
in the minibuffer to enable history completion?

BTW, currently this command highlights the header line only partly.
Here is a fix to keep text properties by replace-match: