The problem is the government isn't putting that money to productive use in an economic sense, and is taking a larger and larger slice of the people's economic

The problem is the government isn't putting that money to productive use in an economic sense, and is taking a larger and larger slice of the people's economic output because that output is shrinking. If the government and the economy were both functioning properly there would be no reason to print money - the treasury would be receiving enough money through taxation. Governments don't go into wholesale printing unless that's not happening. Though to be fair it seems every FR system does at least print around the edges, eventually.