If we are talking about the government using blockchain as means of cost-cutting and being more efficient I think it would benefit the poor overall and the before expense being used before can now be shifted to other projects of the government which will benefit the poor and the needy. But I don't think it will be enough to solve the poverty situation overall as I don't think that the expense being save will be big. Solving poverty will always depend on how big and how will the government manage their budget on focusing amd solving it.
I agree with you. Blockchain could help our Government/economy in cost-cutting as it will reduce or even eliminate the cost of middle man or bureaucratic practices in our Government. Because of bureaucracy, Government employees were able to go into corruption. With blockchain, most of this will be eliminated as it will be blockchain to handle the transaction. Human error will also be lessen. This will not eliminate all the problem but it will definitely help to resolve many problems.