However, you'd still be vulnerable to someone gaining root access on your Vault server. A true HSM uses physically secure memory and a dedicated cryptoprocessor to make it impossible for the secret to ever be leaked, even if the host OS is compromised. This isn't really something that's possible in software alone.
(In fact, the Vault documentation even mentions that you might still want to use a dedicated HSM for security, since they implement a plugable mechanism for secret storage.)
That said... you could use a TPM chip or ARM TrustZone to implement true TPM functionality. It's still a hardware based solution, but it's hardware that's much more affordable and possibly already inside your computer.