Good point re point of failure. If LinkedIn doesn't put a lot of resources into the proxy servers, mail delivery could be very slow or fail completely.
I"m still impressed with the creativity from a technical standpoint.
I'm not overly impressed by the architecture; it's basically a de luxe version of the IMAP push-proxies that were common in the early 2000s, such as Nokia Mail ( I think it was called ).
Phone <------ Proxy <----- IMAP hosts
Same problem; all your lovely lovely communications flowing through the Proxy. And your tasty credentials, too.
LinkedIn have taken the old pattern and injected some data at the Proxy point, enriched from their databases.
Even if it has a lot of resources behind it, if it experienced an outage, the end user would be unaware that their mail service is still up, and since they didn't change the settings, they wouldn't know they could remove the proxy to access their mail until the outage is resolved.
I"m still impressed with the creativity from a technical standpoint.