If you don't care about security, you could just use a browser which ignores invalid certificates.

Invalid certificates are one thing, and you can probably click through that. But maybe your older browser tops out at TLS 1.0, and servers don't offer that anymore (I think the credit card PCI cert discourages it) or maybe your older browser can't do ECC certs and the server you want to talk to only has an ECC cert.

Or maybe your older server only speaks TLS 1.0 and that's not cool anymore. Or it could only use sha1 certs, so it can't get a current cert.

When I can, I like to server http and https, and serve the favicon with HTTPS and use HSTS to induce current clients to use https for everything. Finally, a use for the favicon.