Web browsers are basically the new higher-level operating system. They likely should be using more energy than anything else considering how much we run in them.
An IP address is not always as telling as the DNS name of what you're connecting to. E.g. I may be connecting to a CDN like CloudFlare for content over HTTPS and my ISP will have no idea what I'm doing. But if I used the DNS name that refers to that content it would likely be more obvious in many cases.