Intrinsic. Those people have not been making use of the intrinsic value of Gold, they have been making the same use as in fiat money and bitcoins today, as a rare commodity considered acceptable as a financial instrument. That's (rarity) not an intrinsic value.

That is to say, its intrinsic value includes electrical conductive properties and capacity for use in electrolytic plating. I am ignorant, what are some other intrinsically useful properties of Gold (and Diamonds?)

Well diamonds actually have a ton of useful properties -- beyond just being pretty to look at -- but that doesn't actually justify the price per se.

The problem with Gold is also it's virtue: it's rare. Rarity is good in that it implies value. But let's say you're the American economy and you're growing 2% this year. Should your money supply be governed by how much of it you can dig out of the ground? That is, for example, when South African gold mines were discovered the money supply internationally radically increased, despite having no relationship to economic output. That ends up not working out very well.

Bitcoin though could be thought of more like gold and diamonds not because those things are good to think of as currencies -- they really are not good currencies at all-- but because their all commodities with limited supplies that have markets that move on vagaries with little relationship to any economic necessity or output.

Well diamonds are also valuable because of their use as a coating for cutting instruments. But, much like diamond, your point is solid; gold and diamond have been valuable over the years for the sole reason that people are willing to accept they are valuable.