The CloudFlare blog discusses that idea when they talk about having an "agent process" to hold cryptographic material, but they list drawbacks like having to develop two processes, implement a well-defined interface, and enforce ACLs. I'm not convinced that "developing two processes" is a reason not to do it, since the kernel is effectively just the second process now, but everything else makes sense.
It's unfortunate though since this is one thing I think Windows does decently well. The Windows crypto and TLS APIs do use a key isolation process by default (LSASS) and have a stable interface for other processes to use it [0]. I imagine systemd could implement something similar, but I also know that there are very strong opinions about adding more surface area to systemd.
[0] https://blackhat.com/docs/us-16/materials/us-16-Kambic-Cunni...
TBH LSASS is privileged enough to be a good target for exploits.