If 21M BTC were to replace dollars, with today's distribution, here's the resulting Bitcoin wealth distribution pyramid.

The following chart groups people by net worth, and shows how many BTC each person in each group would receive today, if their wealth in dollars were to be replaced by an equivalent share of 21 million BTC. (I know, this uses BTC that isn't yet available, but this was just for fun.)

Some observations:

1. There are a whole bunch of people with more than 566 BTC. That could one day represent unimaginable wealth, but will also reduce the coins available to everyone else to values somewhat lower than those shown.
2. 21 million BTC will never really be available. Many BTC have already been lost. This will further decrease the BTC values shown on the pyramid.
3. For the great majority of the world's population, their net worth may well be only a fraction of 1 mBTC. People may indeed one day transact in Satoshis.
4. Even half a Bitcoin represents some serious money in this fantasy.
5. This was just for fun, and I'm sure the BTC distribution won't exactly mirror the dollar wealth distribution like this, but there will be a distribution. And it will probably be top-heavy.
6. The $/BTC under these assumptions would be $11,483,190.48.

Appendix:

To generate the pyramid, I pulled some numbers from a few wealth distribution infographics, and made a couple of assumptions. Here's how that went:

Chart 1:

This ends at >$1M, so I had to merge in another chart.

Chart 2:

(Source: http://www.zerohedge.com/article/detailed-look-global-wealth-distribution)

Combining the two, I came up with:

And built the pyramid. Notes:

1. I had to assume average net worth values within the given ranges, but used values that made the total wealth of the group agree reasonably with the available values.
2. The data was for "adults". Anyone can hold BTC, so the BTC/person should probably be reduced somewhat.
3. There was a gap in the second chart, people with $1B - $4.9B are missing. So I fudged a bit.