Declined due to lack of demand for many years.

While we do miss certain item types (radio, checkbox) and basically have menu item type command, I am not quite sure how an Input item type would work.

How do you imagine such control and what would the input do? Do you have an example of such input field in a menu?

For instance, in the context of menu item type radio and checkbox, you can have the following scenario: in firefox, when you right click on the bookmarks bar, the context menu controls the visible toolbars with item type checkbox and those that are visible are checked.