> Mutual-Auth SSL/TLS is a royal PITA, and is basically guaranteed to cause you grief. The client compatibility matrix might as well be considered an NP hard problem to assure yourself coverage, and failure modes of the different browsers/SDKs all differ. As a REST API should have maximum accessibility to clients (i.e., don't wed yourself to any one language/sdk), this is pretty much a non-starter.
Given the inconsistent support for mutual-auth TLS, which along with its direct ancestors has existed for a decade and a half, what makes you think they'll be widespread and correct support for SAS?