By that logic isn't every popular website/service in the world a "DDOS problem" because it attracts lots of traffic?

We're talking about mail. There's an equal distribution of users across many IMAP servers, most run by companies like Google and Microsoft that can handle the flow. Now we're redirecting all inbound mail traffic through exactly one host.

No, this is an opt in service, so only users who enabled this feature are using the proxy.