Does secure hashing imply secure symmetric encryption?
The existence of a family of collision resistant compressing functions does indeed imply the existence of CPA secure, CCA secure and even authenticated encryption. This follows from several classic results in cryptography.

A family of collision resistant compressing functions is also a family of one-way functions.
By the seminal work of Håstad, Impagliazzo, Levin, and Luby (commonly referred to as HILL) "A Pseudorandom Generator from any One-way Function" [HILL99] any one-way function implies the existence of a pseudorandom generator (PRG).
The equally important work of Goldreich, Goldwasser, and Micali "How to construct random functions" [GGM86] had already established that a PRG was sufficient to construct a pseudorandom function (PRF) via the so-called GGM construction.

Once you have PRFs, you have two things. First the classic example of a CPA secure encryption scheme where the ciphertext is $(r,F_k(r)\oplus m)$ for a uniformly chosen $r$. Second, the PRF itself is also a deterministic message authentication code with canonical verification. Using the encrypt-then-mac construction we can then construct a secure authenticated encryption scheme.