When the textbox binding will be removed, the urlbar will be the only consumer of moz-input-box. The only reason the urlbar uses it atm is to add the "Paste & Go" menu item. Instead, editMenuOverlay.js could provide an API/event to add new menu items and the urlbar could use that.
Note that the URL bar's moz-input-box is also used to set role="combobox" and aria-owns on an ancestor of the input, which is required for a11y. We can just use an arbitrary container for this (div, span, whatever), but I thought it worth mentioning that these ARIA attributes on an ancestor are definitely still needed, as I'm not sure we have a test for this at present.