Exactly. That disproves your whole thesis.

No, it doesn't. I didn't say money doesn't store purchasing power to varying degree.

Money is just used as a tool to facilitate a functional economy.

No, barter economies function without money at all, they're just not very efficient.

Currencies with central banks and variable supply have proven to be the best tools at facilitating global trade in a manner that's stable, reliable, and useful.

LOL No. Central banks create the booms and busts. The Federal Reserve was created in 1913 and shortly thereafter inflated the currency supply for WWI. This created an economic boom, which was actually a bubble, often denoted by the period labeled the 'roaring twenties'. The bubble then of course burst resulting in a stock market crash in 1929, which ushered in the Great Depression. Hardly 'stable'.

Revisionist history at its best.

Mmkay.

Income inequality isn't a symptom of a style of currency

Between individuals, no, between entire classes, yes.

[Income inequality is] an inherent symptom of capitalism

Yes, I agree, again, if we're talking about individuals. The inequality is what provides the incentive to work and risk capital...

and bad social policy

No, good social policy. Everyone isn't supposed to have the same thing, if they haven't done the same work and/or taken the same risks etc.

It's not like bitcoin, gold, or any other method of currency would somehow prevent an increasing concentration of wealth into the hands of the rich.

No, but it would better ensure the wealth concentration was well deserved/earned, i.e., by providing some economic benefit in exchange (like manufacturing Model T Fords cheaply, or putting 1,000 songs in someone's pocket), as opposed to an automatic transfer as happens with inflation.