The hashing isn't the point. The leading zeroes method is more likely to produce unreliable results when you can't guarantee the dataset will be large in advance whilst the "keep min M elements" method works fine for unexpectedly small sets. That's why it's used for SZL where the user can request approximate unique counts on any data regardless of size.
Have you read the papers I linked in detail? Some of them, such as HyperLogLog, provide corrections to give better estimates for small sets, and although I can't follow the proof in its entirety, they claim to be more efficient than the alternatives, including the one you propose.
