Why is it recommended to hash passwords with a secret salt?
NIST document section 5.1.1.2 Memorized Secret Verifiers.

That section is a "SHOULD" not a "SHALL".

It is standard practice not to keep the salt secret but to save it with the password hashed verifier.

If the salt is not secret a brute force search is possible if the password is weak such as being on a list of frequent passwords. One example source of such frequent passwords is SecLists.

If the salt is secret such a brute force search will not succeed. Note: stored separately from the hashed memorized secrets (e.g., in a specialized device like a hardware security module) and such a device is generally not available.