Excellent points. Mises himself also addressed many of my questions about money as a commodity later on, in the sections where he considers whether money is a consumption good, a production good, or a third and significantly different kind of good. He settles on the latter, which made much sense to me.

Historically, money has just been a good that everyone (or at least most people) in an economy wants. As such, it is something that you can be sure you can trade for some other good that you want, and therefore you (and your potential trading partners) become very willing to trade other goods for the money good, even if you don’t have any particular use for the money good at the moment. So money is a good (i.e., commodity) whose universal standing as a valuable item facilitates trade. That is, it is a facilitator because it is a commodity.

I will also note that money does not require a third party to exchange to facilitate exchange (though it helps). A dimension of time is a sufficient condition. For example, let’s say you raise wheat and I am a shoe cobbler. You want some shoes, but the harvest is three months away. You might want to promise wheat in the future for shoes today, but maybe I think it’s too big a risk that hail will destroy your crop, or that you will renege. However, you happen to have this yellow metal, gold, that both of us agree is desirable to posess. You can trade the gold to me today, and I know that since you also value gold, I can trade it back to you in three months time for some wheat. Or, even if your crop fails, at least I’ve got the gold, which I value.

I will not quarrel with you that in bilateral economies money is of significantly lower use as a facilitator of exchange. But it could still prove useful in coordinating exchange through time.