Client certificates are a mandatory feature of TLS that any TLS server could request and the proxy would be unable to handle the request, as it (and ideally the

Client certificates are a mandatory feature of TLS that any TLS server could request and the proxy would be unable to handle the request, as it (and ideally the client) has no access to the private key. Therefore, these types of proxies break TLS by being unable to support mandatory features. Separate from that, client certificates are certainly common, being used for authentication, in the US Federal Government, which issues tens of millions of certificates for this purpose as well as smartcards, since George W. Bush banned passwords with HSPD-12.