Can you really not see that any money government employees "inject" into the economy had to be first removed from the economy in the form of taxes or loans?
What difference does it have with the private profiteers removing that money in the form of the tax that is called 'the profit'...
The government employees have to spend that money. That money will move the economy. The rich hoarders that tax the entire economy through 'profit' will hoard it.
At this point it doesnt need to be mentioned how big that private 'profit tax' is and how much economic dynamic it sucks off of the economy.