An authentication method should be selected for a use case based on:

Vault's authentication methods are designed to verify the identity of a client, whether it's a user, application, or machine, against an internal or external system. Selecting the method that best establishes identity (e.g., LDAP for user directories, AWS IAM for EC2 instances, Kubernetes for pods) is crucial for enforcing appropriate access control policies.

While some auth methods are specific to cloud providers, the cloud provider itself is a factor in *which* identity can be established, not the primary decision driver for *how* identity is established in general.

Cryptographic hash strength is relevant for secure password storage *within* some auth methods, but it's not the overarching criterion for selecting an entire authentication method.

Auth methods and secret engines operate independently; a secret engine can be used with any authenticated client, so compatibility isn't a primary selection factor for the auth method itself.