You don't want to pay $1/month to store a single secret. You want a nicer workflow for creating ephemeral users and tokens than AWS themselves have. You want to do on-the-fly encryption of all sorts of things. You want a real PKI without every bit of know-how.
It’s 0.25 cent per month to use the Secrets Manager and you can store multiple key/value pairs per secret. If you’re not using the automatic key rotation, you can store a “SecretString” in parameter store for free for low volume usage or for higher volume It’s close to free.
Besides with vault you now need to set up a cluster for HA. But is your time worth nothing?
As far as users and tokens. That’s what Cognito is for for external users or associating your AD with IAM roles for internal users.