Beach sand (sold as play sand) has a superior outcome in concrete surface restoration based upon my experience and experimentation in Missouri, US. Choose a sand which is pre washed, or wash it, and sieve it with a fine screen even it comes as pre-screened. This sand is rounded like a desert sand, but perhaps the comparison ends there.
Now, let me try to answer why desert sand is not well suited for making concrete. It is more rounded or spherical, offering the least amount of surface area for bonding to cement for a given volume of single grain.
On the other hand, rougher angular sand may offer surface area several times that of rounded sand. This multiplying factor can actually be huge, way beyond ordinary imagination, given the way microscopic nature works.
One may also imagine compaction of angular grains to something like cold working of metals which makes the metal crystal grains parallel, increasing the hardness.
Therefore, bursting strength of a test cube made purely with sand and cement is likely to differ perhaps exponentially (or a function resembling like that) in relation to the surface area of an average sand particle in that mix.