Answer:
It really depends on the state of the economy but I'll give a general answer, Investing in a bank is pretty much investing in people, when the economy is good the banks are good, and when the economy is bad the banks are bad, namely stocks. If the government were to invest in banks and give them money they would wouldn't be circling the money into resources, technically the government doesn't really need to invest in banks anyway since they are the ones that print the bills and give money, investing in banks is just pointless when the government already pays for your job, in which YOU give money to the bank to either save up and spend the money later, or to invest in a trust fund which also circles money back into the government through taxes.
Step-by-step explanation:
If the government already pays for peoples food , jobs , etc and expect them to put that food back into business and then tax the people and the business why would they need to invest in banks? Unless of course there was a stock market crash and the government needed an incentive to get people to buy stocks and thus started to invest but that always goes bad.