If you have the sort of system that has automated key issuance and low interactivity on hosts, I agree that makes sense. But then, that's exactly the 'ssh as yourself and then sudo to root' model, just abstracted in a different way, isn't it? In both cases you're authenticating to some intermediary as yourself first and then being given access to the local root account—it's just that in my system the 'intermediary' is a local unique user account, whereas in yours it would be the individual authenticating to the temporary-ssh-key-issuance system like Vault. As long as that system does a unique authentication, the two are more-or-less identical, although you'd have to be careful to ensure you can untangle the auth logs to the intermediary system and associate them with local root sessions.
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If you have the sort of system that has automated key issuance and low interactivity on hosts, I agree that makes sense. But then, that's exactly the 'ssh as yourself and then sudo to root' model, just abstracted in a different way, isn't it? In both cases you're authenticating to some intermediary as yourself first and then being given access to the local root account—it's just that in my system the 'intermediary' is a local unique user account, whereas in yours it would be the individual authenticating to the temporary-ssh-key-issuance system like Vault. As long as that system does a unique authentication, the two are more-or-less identical, although you'd have to be careful to ensure you can untangle the auth logs to the intermediary system and associate them with local root sessions.