And why, exactly, total value of currency should equal total amount of wealth? What exactly is the contradiction, arbitrage or other mechanism that sets total value of currency to total amount of wealth?

It's not, actually - the total value of all physical $USD (M0) is only about $3.8T, vs. the figure of $100-300T given for total wealth (which seems low to me, BTW).

The actual truth is even weirder: if Bitcoin takes over as the world currency, its value in $USD will be infinite, but the question will be meaningless, as the dollar will be worthless. Currencies tend to be winner-take-all within a society; if one takes over, its rivals lose all value, as their only value is in being a medium of exchange and store of value.

This is perhaps a contributory factor to the Bitcoin's volatility: if you actually believe it's going to succeed, unambiguously, the rational thing to do is to move all your wealth to Bitcoin. And similarly, if you believe it's going to fail, the currency by definition is worthless.

There are 164 national currencies in the world. The USD is the defaco world currency and the USD is not worth infinite of other currencies and the rest are certainty not worthless.

I think the US government tolerates crypocurrencies because realistically they are far more damaging to countries like Venezula and China who have much more restrictive economies and in those countries the flexibility of bitcoin is a huge advantage.

How many aircraft carries does bitcoin have? 0. Which (in my opinion) happens to be the exact same chance of bitcoin usurping the USD as a global currency short of some fundamental change in world power.

The thought experiment explicitly implies BitCoin usurping the $USD as a global currency, and presumably all other ones as well. I'd agree with your assessment of which countries/currencies are realistically much more likely to suffer, but thought I'd engage with the thought experiment on its original premise.

On the aircraft carrier issue - the killer app (literally) for cryptocurrencies is autonomous weapon systems. Imagine if you could deposit $Xm Bitcoins into an address and have access to a fleet of 100,000 drones on 10,000 speedboats. At that point, we're really in uncharted territory, though.

The original assumption was just world cash supply (M0), include all m3 supply and you in for a surprise.

Who creates money is the best answer to your questions.

You mean (US) M3 equals (US) wealth? Why? Can you back that claim with statistics?

Does anyone think the current owners of capital are going to sit by and let their powers and wealth be destroyed? If bitcoin were ever likely to become close to being the dominant payment system it will be outlawed with "extreme prejudice".

Do the current owners of capital principally hold their money in cash? If they're holding their money in ownership of companies and things, then their wealth wouldn't be destroyed as (current) monies became displaced by bitcoin.

No they mostly own assets, but they need control over the money supply to ensure they don't lose control of the assets. How would the GFC gone if they did not have control of the money supply?

I'm not convinced. If I own a row of houses, bitcoin displacing dollars won't change that.

If you just own a row of houses you are not part of the 0.01% who are in control of the money supply.

If I own so many houses (or other such assets that aren't simply a pile of dollar bills) that I'm part of the 0.01% (since you've changed the argument from "owners of capital" to "0.01%"), the dollar being displaced by the bitcoin as currency of choice doesn't change that.

It does when the interest rate you have to pay on the mortgages you have over the properties can no longer be controlled. If you were the owner of many houses in 2007 and we used bitcoin rather than dollars you would have been in for a world of pain.

Nah someone just needs to gift Donald Trump a fat stack of it and it'll be recognized as genuine legal tender in no time.

I think Bitcoin has potential but the majority of people do not want their everyday currency to change value everyday

Every currency changes its value every day. Every minute even.

Plus I don't think anybody would mind if their currency tends to increase in value.