I usually don’t use one for browsing, and not for privacy reasons.

I have a wireguard hub-and-spoke configuration with my VPS as hub to

• Let my VPS act as a reverse proxy to my home servers
• Not have to expose ssh on my VPS to the public internet
• Easily reach all my home servers when I travel
• Route traffic through my VPS when I’m on sketchy open WiFi. Which is when I’ve encountered OP’s sign-in requirement.

Happens to me only when I use my VPN.