Then, there wouldn't be just 0.0000001BTC per person. 21M coins divided by 7,800,000,000 people is about 0.00269 per existent person. Bitcoin is way easier to be moved around in much smaller quantities - you can't pay with 0.0000001$, can you?
The global wealth disparity will be a thing no matter how much we change things. There'll always be someone who earns more (or steals from others). We can't really change that unless we apply communist rules.
The global wealth disparity doesn't have to be a thing. It's only defeatist propaganda you've been fed that makes you believe so. Similar to how creating a currency not owned by a central bank is not a thing that caught on until bitcoin. People who earn their money are not the issue, one could argue maybe they pay more taxes etc. but thats to be decided. The issue is with people who don't earn their wealth- either through stealing as you say or simply inheriting.
This unearned wealth creates the issue because most people would reward someone for doing good. Almost no one would reward someone for doing nothing or worse hurting others. Yet in most parts of the world the wealth is held by people who were friends with kings, dictators, etc. from the last few centuries. I am not especially into choosing an economic side, I just believe we should develop the best system from the ground up. Rather than using a system biased by history to determine who is the wealthiest.