Hal Finney’s ‘thought experiment’ - help needed

To those that are familiar with Finney’s question from 2009:

“As an amusing thought experiment, imagine that Bitcoin is successful and becomes the dominant payment system in use throughout the world. Then the total value of the currency should be equal to the total value of all the wealth in the world. Current estimates of total worldwide household wealth that I have found range from $100 trillion to $300 trillion. With 20 million coins, that gives each coin a value of about $10 million.”

I have a fundamental question. If Finney’s scenario came true, then wouldn’t the value of all wealth in the world have doubled? (i.e. $200tn-ish of household wealth, plus Bitcoin now valued at $200tn) Ignoring inflation, isn’t that outcome impossible?

I’m really struggling with getting my head around that scenario, unlikely as that ultimate outcome might be. Any insights would be much appreciated. Thanks.