Key derivation functions use hashing functions internally. The best and clearest example of this is PBKDF2 where you can also pick the hashing function that you'd like to use (this is typically PBKDF2-HMAC-SHA256 but can be changed to use other cryptographic hash functions).
Argon2 internally uses BLAKE2b (see 3.1 in the Argon2 specs) which is more performant than SHA256 and most common hashing functions.
BLAKE2b is optimised for x64 platforms which fits exactly the requirements of a password hashing scheme. SHA512 would also be ok, but SHA256 would be much slower in software and due to the fact that SHA256 is used for Bitcoin mining, custom hardware for SHA-256 is very cheap – this is exactly, what we do not want for a password hashing scheme.
So, in general, in itself you'd not get a major improvement security wise over plain Argon2 - which, despite being a relatively recent algorithm, it meets all requirements of a password hashing scheme and has been vetted by the crypto community.
There's an article on Medium that better explains why you should use Argon2 100% of the times on new systems.