Bitcoin itself is not a magic stick, it can't do nothing if people don't do actual work. I think that the answer to the question how bitcoin and blockchain can help poor countries lies into the governments of these poor countries. They can use the opportunity and create a business friendly environment for Bitcoin and blockchain related businesses by offering companies low to zero tax rates and a high quality personnel inside the country. I think that countries can spend money on educating their talented citizens about Bitcoin and blockchain technologies and make a very good developer out of them.
It's a tool for sure, but not a solution, here I agree with you.
Clearly, to use such a tool, a country should have everything in place to make it happen, including the frameworks, infrastructure, and the desire to not only to profit from their citizens but to give them alternatives and abilities to work with the tech in their own ways.