Yes, a proper National Bank as the "baseline" and guarantor of economic liberty, bound in all the same ways as the government and specifically forbidden from more extensive profitable behaviors, would do much to smooth flaws of capitalism.
In the US, this would basically just be making the Federal Reserve actually government owned instead of a corporatist shitstain, and forced to allow individual loans and accounts instead of existing to be a bank for the other banks.
Both you and Doomsought are misunderstanding: Banco do Brasil is (nowadays) a run-of-the-mill commercial bank, which has the government as its major(but not single) shareholder, not the Federal Reserve(the Federal Reserve role is played here by the Banco Central, which is part of the federal government). The point of the Economy Minister is that the Banco do Brasil is by itself a giant conflict of interest, so it should be privatized, especially since there already is another (fully)State-owned bank that covers the social side of financing, the Caixa Econômica Federal.
Also, Morphic Tide, what you are proposing was what used to be done in Brazil; before the creation of the Banco Central, in 1965, the Banco do Brasil was the Federal Reserve, as well as being a commercial bank. What happened? Since the Banco do Brasil had a direct line to the Treasury, it was used to 'lend' money to all sorts of 'friends' of the people in government. Of course, this 'loan' was never repaid. The government then had to print money or raise taxes to cover the deficit. Trust me, having the Federal Reserve as a corporatist shitstain is less worse than having her as the 20-dollar whore of everyone who has some sort of connection to the government or government members.