TLS client certs were unpopular way before external TLS termination became popular.
Besides, it would be fairly easy to implement at a cdn layer. Just give it a list of valid CAs, and have it set some header.
The real reason is that UI challenges for client certs are really hard. You can see it in the fact that people actual do use client certs in server to server communication (e.g. like between cache and backend)
