I'd like to see DNS ownership combined with the time range and an owner-unique key so you can go to the website you intended to visit rather than whoever happens to own the domain at the moment.

Why would they still have the server but not the domain?

Domains cost money to maintain. They can lapse, change, or be sold. Sometimes people make mistakes. So to my way of thinking they're great as a short-term named identifier but not as a long-term stable identifier. Would be nice to have both.