For me it is not about wealth it is more about knowledge and financial management.
People could use Bitcoin or crypto whenever they want, but they should know how to handle or manage it (Risk Management).
A lot of things are involved in the decision making, knowledge of how bitcoin works and how it can be traded without buying at the wrong time - seems very simple but goes wrong at the wrong time when the quick decisions are taken.
Financial management is a more broad term where you have to keep a long term goal. It is more applicable to the mature group of people who are trading for long time and are managing different asset classes easily with good flow. Should be started from the newbie stage though.
Bitcoin will give the financial stability so to eliminate the poverty you are talking about is to invest in bitcoin although, in this modern world, there is no typically or remote area that there is no internet service. The only thing you can say is that the internet in some rural areas are facing network issues. Which probably a slow network issue.
Elimination of poverty will no happy by just a magic bullet which you assume to be bitcoin. Poverty stems from a large number of factors which need to be worked on first before the people's lives can be improved. It is not going to happen overnight.