Not publishing the dataset is becoming less common as we start inching our way slowly to reproducible science. Public code with public data is the simplest form of reproducible research, where we can re-run your experiments with the same code and should get the same result (modulo some extremely low-level randomness or hardware differences that we may not be able to control).

That alone isn't enough to kill a paper, but it doesn't help. As another commenter said, showing your approach on public datasets and other approaches on your dataset will help, as it gives the rest of the community something that is reproducable.

It's more common in medical venues because of a few reasons:

1. Difficulties around safely releasing medical data. Proper anonymisation and informed consent.
2. It is more common in medical science to go for a higher level of reproducibility, where the same or a similar study will be done on a different population (i.e. same method, different data). This is pretty uncommon in ML, it's hard to get papers accepted in this format.