Well, you failed to clarify the intent of your statement.
the current model is outlined in the Original Post, but I'll repeat it for you.
Well, I don't think you've got that right.
Sand is mostly quartz. The reason for this is that
chemical weathering (not, as you seem to suggest, mechanical weathering) dissolves the other minerals in granitic rocks or (in the case of feldspars) converts them to clay.
Quartz is extremely resistant to chemical weathering, so the grains of quartz remain and are transported by wind or water.
This, by the way, explains why there is a maximum size to sand grains --- they have an upper limit set by the way that granite crystalizes as the granite-forming magma cools.
Mechanical weathering, and freezing in particular, plays a relatively small part. (You can tell how large a part mechanical weathering and erosion has played by looking at the composition of the sand: more mechanical weathering and erosion corresponds to a higher proportion of non-quartz material such as feldspar.)