I would point out, though, that the disadvantages listed against Secrets as a Service need not apply to Hashicorp's Vault:
1) Single point of failure: Vault Enterprise offers high availability solutions that should be able to mitigate much of this (at a cost, of course).
2) Codebase must be changed: Vault (and Consul) really shine here: Consul Template -- and Envconsul -- can be used to seamlessly integrate legacy code with Vault.
3) System-level access must be protected carefully: Well, this is always true, but Vault gives you more options than many others here as well: based on risk assessments, you can choose to limit the secrets you issue, particularly when you're talking about system-level access. You can have very short TTLs, one-time-use wrappers that limit the exposure of said secrets, etc.
(I don't mean to sound like a shill, BTW. It's just that these points easily jumped to mind, having just certified as a Vault Associate. YMMV. :-) )