I think Bitcoin can help a poor country or nation by protecting it's asset from hyper inflation and economic collapse and that if the country invests on it just like what El Salvador, Bhutan and some US states did. Bitcoin being a decentralized asset to a specific country will ensure it's people that the said asset is safe and secure.
It is not as easy as you make it seem. Even if the country were to invest in Bitcoin, it would take years for that investment to mature before the country starts seeing the benefits. Don’t forget, the country is poor, so whatever amount they invest will have a significant economic impact on the country in the meantime.
A country does not need to invest money in Bitcoin in order for Bitcoin to help its country especially when the funding of the country is not sufficient enough for its local/nationa projects. All the government need is to stimulate blockchain investors and company to invest in their country establishing crypto-related infrastructure. To do that the government must tailor their regulation in favor of cryptocurrency. They should create Bitcoin friendly law and welcome the adoption of Blockchain technology. The result of this move is way faster than spending government stash to invest in Bitcoin because once all is polished and deals were made, the development of Crypto industry on the country will start to initiate thus giving job opportunities and investment opportunities for people. As I stated on my previous reply, government then will enjoy taxes both from the company and the people who happen to get jobs from these collaboration.
Individuals can invest in Bitcoin to help themselves, but as a country, they need to diversify their economy, create multiple streams of revenue, create employment opportunities, and adjust their economic policies to accommodate both local and foreign investors. There is a lot of work to be done to eradicate poverty in these poor countries. Bitcoin alone cannot do it.
Yes, there are a lot of things to be done, and Bitcoin can't help if the government refuses to accept its adoption. In fact, the government needs to do all the effort and use Bitcoin as a tool to improve the way of living of its constituents.