Oh yeah, because assumin maximum values in your domain doesn't move all algorithms into constant time and renders complexity theory void.

It doesn't though. How would merge sort become constant time if you assume a maximum value? It's also a joke...

The main "value" in the domain of sorting problems is the number of elements in your collection.

A subproblem also considers the elements to be integers, then they become another "value" domain. (But in general, sorting problems only need their elements to be comparable, not necessarily integers.)