I suspect they added up those hundreds of billions
By looking at the amount of credit and average interest rate, and ignored pesky stuff like expenses, salaries, reserves for bad debt, etc.
Obviously banking is profitable, this is just arguing about how profitable. The idea is "if the government is the bank then the government gets that profit". Well, that's nice but as Tim says you have the little problem of the government deciding who gets loans - do you really want a situation where someone gets a $100 million loan to build a skyscraper based on being the friend of a politician in charge, rather than because he's got credit / business plan / whatever that a bank thinks will be profitable for them?
Maybe a school chum gets to be a high government official, so even though I have no experience with such things, I've got a big loan and am paying myself $1 million a year to be CEO of a corporation building a skyscraper. I don't care if the corporation fails and the building is never finished, or is finished but never gets any tenants because it was built in the wrong place, because I'm still making $1 million/yr for a few years before that failure becomes apparent! This sort of thing has been happening all over China, because that's how a lot of loans get done over there.
You can capture some of that profit via taxes. If you want a bigger share, you can have higher taxes on banks, but you will cause there to be fewer banks and less credit being issued because the bar for profitability goes up when taxes get higher. Most people don't think that's a good idea (or at least they don't think its a good idea if it means their access to credit becomes more difficult)