I've never witnessed or experienced there being a defficiency with mud tread tires in sand. They seem to work just as well or better than all terrain type treads.
In fact, practically all dirtbike and atv/utv tires have much greater resemblance to mud tread tires than any other tread type. There hardly exists a dirt bike or atv tire that has any resemblance at all to an all terrain tread tire.
And if you think of sand paddle tires, with their giant, wide spaced tread blocks going across the whole width of the tire, they have more in common with large blocky wide spaced mud treads, than closely spaced all terrain treads.
I've spent plenty of time driving and riding in dune sand and sand washes, with lots of various different vehicles, and with others about with many more different vehicles. I've not seen anything that would suggest that mud tread tires are bad in sand.
I don't buy it that an all terrain beats a mud tread in sand.