Vault attempts to mitigate this with its 'seal' functionality, but in practice if an attacker gains access to a running Vault server, and/or the cloud provider account it's running in, there are many ways that secrets could be exposed.
EnvKey allows you to avoid trusting the host server, full stop.
Here's a good example: https://github.com/slingamn/vault-exfiltrate
The Vault docs include a list of 'hardening' steps for secure production usage. These are great steps to take, but each one represents a mistake that could be made. And because the Vault process is trusted with plaintext secrets, the stakes are high. Making a mistake could lead to a compromise.
With EnvKey, the host server is never sent secrets in plaintext. For defense in depth, we also follow best practices for hardening our networks. But I think we've seen with Okta and other incidents that despite best intentions, best efforts, and strong engineering, trusting the host server whatsoever just isn't good enough anymore.