There's a flaw in your logic here because there's nothing that stops anyone from using the Dollar or the Euro or the Yuan or the Pound or the Yen or any currencies.

The only limitation - and applies to cryptocurrency as much as fiat currency - is the ability for each person to earn some. And earning power is mostly correlated with one's ability to offer a good or a service to someone else, it's correlated to skills. Bitcoin can't give poor people more skills. And the fact that Bitcoin is divisible to the 100 millionth unit doesn't make a poor person better able to afford the goods or services in their market.

The ONLY way for "Bitcoin" to alleviate poverty is if it creates new ways for people to earn money, new jobs.