One thing that makes it less surprising is that there are lots of numbers which map to the same result - for example all permutation of a bag of digits. I check

One thing that makes it less surprising is that there are lots of numbers which map to the same result - for example all permutation of a bag of digits. I checked, and there are only 55 distinct results (54 excluding 0000) from applying the process to all 4-digit numbers, which leaves less space for lots of cycles.