If it wasn't considered a solved problem, we wouldn't have public CA's for our browsers to trust, as their very premise is based on having a secure way to store

If it wasn't considered a solved problem, we wouldn't have public CA's for our browsers to trust, as their very premise is based on having a secure way to store private keys. I think a FIPS-140-2 level 4 HSM and hashicorp vault enterprise will cover 99.9999% of all other use cases for private CA's and PKI.