Everyone using a browser that doesn't get security patches is basically a walking malware farm. Not supporting them with your site and pushing them to upgrade is the moral high ground.

This. In fact by supporting those browsers on your website, you're in effect complicit in allowing malware to hijack those users' logins.

It's a good first step though. This means that websites can start telling users "we don't support this browser because Microsoft doesn't", etc., and they will die off quicker.