Not a good idea for CI tests. It will just make things flaky and gum up your PR/release process. Randomness or any form of nondeterminism should be in a different set of fuzzing tests (if you must use an RNG, a deterministic one is fine for CI).
then it actually is a huge success
because it found a bug you overlooked in both impl. and tests
at least iff we speak about unit tests
The whole concept of allowing a flaky unit test to exist is wild and dangerous to me. It makes a culture of ignoring real failures in what, should be, deterministic code.
So, yes, logging the inputs is extremely important. So is minimizing any IO dependency in your tests.
But then that runs against another important rule, that integration tests should test the entire system, IO included. So, your error handling must always log very clearly the cause of any IO error it finds.