Persistent identity is fine, it just doesn't belong on individual servers. If the data matters, then it's better for it to be reproducibly managed, durably persisted, etc.

For many database needs, there are great options that natively support a highly available cluster.

For those needs that don't have a good clustering option, there are great network storage systems that are easy to deploy and use.

You don't need to treat hardware as a pet to have a database with persistent identity.