Enable "Search" field on ContentReference and ContentArea pickers

When you click "Add content" on a ContentArea or ContentReference, you can select an item from an item tree. This is not always comfortable, especially when the page tree has a large number of eligible items. It would be good to have a Search field there, that would search at least by name in the tree of available items. This functionality is already implemented in CMS for LinkItems' content pickers: see lower part of attached screenshot - so maybe it is possible to optionally enable it on CR and CA pickers as well
Currently it is not easily achievable (without dojo custom module) to add this "Search" field to CR and CA pickers. I propose either adding it to every picker, or creating an EditorDescriptor property/setting to have it.