At uSwitch we use Vault to generate short lived database credentials for our applications running in Kubernetes. We wanted to move from an environment where we had 100 dbs with a variety of static passwords being shared around to a place where each pod would have credentials that only last for its lifetime.
We chose vault because:
It had built in Kubernetes support so we could use service accounts to permission which pods could access which database.
A terraform provider so that we could configure both our RDS instances and their vault configuration in one place.
A variety of database providers including MySQL/PostgreSQL (our most common dbs).
A good api/Go -sdk so that we could build tooling around it to simplify development worfklow.
It had other features we would utilise such as PKI