Ah man, you were so close. Reasoning decently and writing well up until the last sentence.
No, that's EXACTLY what the measuring stick suggests, because an hour, yard, or kilogram is always that thing IRRESPECTIVE of what else happens. A bitcoin doesn't buy you a fixed amount of anything, because money is a fluid negotiation of real things always in flux.
Your example is great, and a fixed money stock takes away one sort of potential fluctuation.
Does it make prices stable, more "fixed"? Probably not. If anything, makes it less predictable than gold, less ingrained than fiat
