Of course sorting floats happens a lot. In practice one rarely encounters NaN's and ±Inf's, so fast comparison for concrete values is the default. I don't know why the 'slow' total order is not implemented in hardware though.

But fortunately in comparison sort algorithms that run in O(n lg n) you can get away with doing an O(n) partitioning of the array into [-, +, NaN] and then applying a fast integer comparison operator to the negative values (-) and positive values (+).

In fact the above idea ties in neatly with QuickSort, which is already based on partitioning & sorting recursively.