(In the specific case of TLS, I get additional warm fuzzies from being sure that, however screwed up the web server is, it cannot be confused[1] into revealing the secret keys when it does not have access to them in the first place. I don’t know to which extent this is actually important, though. A factotum[2]-like approach is a compromise that gives the web server the ephemeral keys in exchange for not having to pass the entirety of the traffic through the terminator, but I’m not aware of any practical implementations except for the one Akamai, disgustingly, patented[3] 10 years after the actual invention.)
[1] http://www.cap-lore.com/CapTheory/ConfusedDeputy.html
[2] https://www.usenix.org/conference/11th-usenix-security-sympo... or http://doc.cat-v.org/plan_9/4th_edition/papers/auth
[3] https://patents.google.com/patent/US9531685B2 (wow, I though this was the Cloudflare patent, but that one, https://patents.google.com/patent/US8782774B1, is even more trivial)