Your points are well-taken. However, though the Yamnaya were pastoralists, they emerged from an agricultural population after, and probably as a result of, the increased mobility due to the invention of the wheel. (Cf. the shift from agriculture to nomadism in the Plains Indians after the introduction of horses.) Prior to that time, most of the steppe population lived in river valleys, and - conceivably - the ancestors of the Yamnaya acquired partial immunity then.

Speculation, of course. Reich devotes only a single paragraph to the possibility.