Replace hashing function with asymmetric cryptography when password authentication


I would like to know if the following ideas are feasible:

Hash function is one-way function.

Generate public key from private key is irreversible(asymmetric cryptography).

User password entry -> SHA(or adding salt before hashing) -> hash value(as ECC private key) -> generate public key from private key -> save public key(drop private key)

Password authentication:

User password entry -> SHA(or adding salt before hashing) -> hash value(as ECC private key) -> generate public key from private key -> verify the public key with the saved one.

Based on that:

a.User or others can encrypt selected information(by using public key) that only user can decrypt it.

b.System administrator can generate a public/private key pair then both user and administrator can encrypt/decrypt selected information(by using Diffie–Hellman key exchange method).

I think that brute-force method(exhaustive attack method) can crack any password, and it is only a matter of time.It should be an another topic.

I am trying to prevent user information leak or rainbow table attack even if system being hacked.

I have searched and read the following information:

https://crypto.stackexchange.com/questions/9813/generate-elliptic-curve-private-key-from-user-passphrase

Handling user login using asymmetric cryptography

Asymmetric Cryptography as Hashing Function