Time for a National Bank?

I'm trying to understand this. The banks get in trouble because of bad lending practices exacerbated by securitization. They stop lending. The government swoops in and gives away piles of money to induce the banks to lend. The banks don't lend because they can't find credit-worthy borrowers. So instead, they take the money and use it to shore up their own balance sheets. But if the banks aren't lending, they're not making money, and therefore their health is still very much in question.

Since the banks aren't lending, businesses can't get loans. This puts them in trouble and makes the weak economy weaker. So the piles of government money aren't doing anything for the general economy. For the banks themselves, the money is doing nothing more than insuring that they will eventually need more money to postpone their collapse again.

Wouldn't it be better for the government to cut out the middle man, forget about giving money to the banks, and instead loan it directly to businesses and consumers? In other words, why don't we set up a national bank?