Why is this not an amazing idea when all our governments are drowning in debt?
Because it will halt the growth of the non nationonlizd banks. They won't be able to compete with those rates, so who in their right mind would do business with them? Then you have people with a better interest rate, helping individuals and helping the economy yes, but on the flip side, you hurt a lot of banking institutions, which hurts a lot of employees. A lot of banks will go out of business, people lose their jobs, can't pay a loan that they have even a good rate on, etc. Other banks will cut back on employees out of necessity this translates into less care for the customer, and usually less wage increases for employees. It suffocates the private banks.
In a couple of decades you will have a culture where the small banks simply can't compete with government incentives given by the government bank, since the government can redistribute monies from other sources as well to bring down their own rates even more if need be. At that point, the government essentially has a hold on the whole market, and when the majority of the smaller banks die off, you don't have any alternatives, you have to pay their rate, whatever it may be, and they will be raised gradually, since it's a back door way of taking in money without raising taxes.
Those monies will then be redistributed in other areas.