What I'd like to see are searchable drop-downs (not to be confused with text input with suggestions).

And the date/time picker controls are too limited for many applications.

Do I understand that first one correctly as datalist without allowing the user to submit a value not on the list?

That, and how it's rendered needs to be separate from the value the the input gets. Just like `<option value="123">John Doe</option>` or ideally even rich html like `<option value="123"><small>123</small> John Doe</option>`.

I guess the best way to render it would be exactly like `<select>` when closed, but when opened there should be a search box where it'd normally show the first option.

Clicking search would call a javascript function, which could then adjust the set of available options via the standard DOM APIs.

Alternatively they could add support for a special element `<selecthead>` which can contain whatever you want, which would render fixed at the when the drop down is opened and can be interacted with like normal html elements. Then you could place your own search fields inside.