In the current contact discovery implementation you need to fully trust the server, namely the open source component that is the contact discovery service.
In this proposed new implementation, you still have to trust the server; you need to trust closed source processor hardware offering the Software Guard Extensions.
Those extensions need necessarily be kept away from user control, because otherwise you could pretend to attest a particular program, while actually running a different program. So this encourages a centralization of trust into a private key managed by processor manufacturers, which with server hardware is primarily Intel.
(note that you fully need to trust the processor hardware in both cases; I'm only arguing that this scheme possibly isn't an improvement)
Could anyone shed some light onto why this is an improvement, assuming you don't trust the CPU manufacturer? This is kind of the premise of the article, which notes that "more fundamentally for us, we simply don’t want people to have to trust us", "that’s not what privacy is about".