I appreciate your authoritive opinion. Folks tend to not believe a poor old dumb hay farmer.

Just because the breeding farms of Kentucky, and the Racing Stables of New York & Florida use a lot of alfalfa hay, does not mean horses used for light recreation need alfalfa.

Upon consideration, if thick stems are their problem, the problem may be climatic. The further north, the longer the Summer Days the taller alfalfa tends to grow.

At least one breeding farm in KY runs one or more stockers with the horses, to graze down the grass that the horses reject.
They put their horses in a stable for the night with timothy hay for bedding. (Not wood shavings, or special Ohio wheat straw). When the horses stop grazing on their bedding it is hauled out and fed to the cattle.
The cattle get enriched hay as well as enriched grazing for their diet.