Websites should obviously not be allowed to shrink or remove the scrollbar. The reason for this is because people like being able to scroll so that they can see the rest of the page.
Hear hear! There's a website I use that has made the scrollbar so tiny it might as well be invisible. It's certainly unusable. It is an absolutely pain and I don't understand the choice on their part, but if there was a way to prevent it browser side that would be amazing.