realistically you would want to use a merkle tree to hash the source, to make it more secure against a chosen plaintext collision, but aside from that this'd be a great addition.
... and it's impossible to know for sure that a hash is secure against collisions. For example, MD5 was the standard for hashing for quite some time but is considered broken today due to attacks that have since been discovered. By implementing the hashing using merkle trees, you increase the avalanche effect relative to the data, making it much harder to force a collision.
Obviously any compression function has collisions - this is a mathematical fact. What I mean with "no secure hash function has collisions" is that if you are using a secure hash function you shouldn't need extra defenses against collisions attacks as the "secure" in "secure hash function" implies those attacks are infeasible.