It's not impossible to have a O(N) sorting algorithm if you add more constraints, e.g. use operations other than comparisons.

Most people would be fine with a hybrid radix sort for day to day use.

You only ever have to move every element once to get a (pre-known) permutation that represents the sorted list.

The problem is the information in a permutation (n! possible orderings) and one can only ever "throw away" half of them on every comparison, leading to log_2(n!) or nlog(n).