Well, the entire world economy doesn't need to go Bitcoin. However, if even 1% of the world economy goes Bitcoin, you have an amount equal to a few thousand percent of the current market cap.
You ever consider how much it would cost to secure a "$20 trillion+" POW network? Taking into account that it costs ~25BTC/10 mins to secure it now, when the market cap is a mere 10 billion?
It would still cost 25BTC/10 minutes (or more likely a significantly lower amount as more than two more halvings are likely to have taken place) But the purchasing power of 1BTC would have increased dramatically.