When you say "icon" here, are you talking about the combo box arrow, or icons on the items themselves? The latter are often useful if you have items of different types in the same list.
I think we should have the combo box arrow, to show the user they don't have to type if they don't want to.
I'm talking about the combo box arrow. I think that's fine, but in that case users shouldn't be able type, they should only be able to select from a group of options, like this:
From what I understand, the text field where a user can type in is for searching through options available to them. If we know that people tend to search by typing more than scrolling, we should use the precedent for type ahead dropdowns.
If people don't typically type to search or there are usually only a few options, it can just be a dropdown.