This functionality could be automated with a browser extension, or even as a built-in feature where there isn't an EV cert.

Then your whois provider gets to see all the domains you are visiting in real-time.

Good point. Even though your ISP/DNS provider can see this too (including HTTPS connections) it's prudent to limit data leakage as much as possible. Perhaps the lookup could require a single click (only needed when you are unsure of the owner).