Abusive monopolies without the imposition of violence (either by the government or the company) lasting for a long time horizon? Yes, that would seem implausible in a free market. For example, if someone controlled the water pipes and charged a $1000 for a cup of water, then someone would find a way to bring in water for less and would start contracting to build their own pipes, maybe locking in long term contracts with people given the time horizon of construction. That threat alone keeps the prices low. But I also live in a city with city run water and sewage where the infrastructure is falling apart and the cost is on the order of 2k a year for normal water usage and actually would be about 1500 if no water was used. Sewage overflows, water goes brown and federal intervention is required. So a little competition might actually be useful.
As for pollution, have you looked at the history of state run industries and their pollution record? How well does the US military manage its pollution, particularly prior to the EPA when the public consciousness shifted? How many of the worst private polluters were in the service of the government (such as for the military)? There are also tales of the communist countries and their abuse of the environment. And in the context of a democracy, one would assume that if it is faithful to what people want, then to have pollution controls requires at least 50%+ of the population to want them. That sounds like a strong market incentive to provide that not to mention actual destructive pollution can be subject to claims by those injured by the polluters. While it was before the largest amount of industrial pollution, there was a time in the US before the government got involved where pollution was restricted by such considerations. Companies did not like that so the government started to regulate in order to protect the polluters. Time and time again, actual government legislation is used to either protect the guilty or it comes in when 90% of a problem has already been resolved.
Also, the first two economic schools of thought you list do not make any basic sense. If it is just spending, then why would there be boom bust signals? Why doesn't everyone just keep spending? Something else must cause a reduction in spending which ought to be pretty important. If monetary supply is the only control for the economy, then set it and forget it on the trajectory you want. Since there doesn't seem to be a stable path, then some other factor is important to consider.
For either of them, why not just print up a million dollars for every person? Do you suddenly have a supply of million dollars worth of goods for everyone? No. There is real wealth that has to be produced and that is why futzing around with money is not good enough.
The information coordinating function is that of prices which requires a relatively stable money supply for accurate signals. If the money supply is artificially tampered with, then the entrepreneurs make bad bets, thinking that either there are more resources then there are (inflationary monetary supply, boom period) or there are less (deflationary monetary supply, spending contraction). The first case leads to half-completed projects when actual resources run out across the economy (bust). This leads to recession/depression which is a time to realign the resource allocation to what is actually desired if government stays out of the way. Compare the 1920 economic downturn (hands-off government, rebounds quickly) to the 1929-1940s economic depression (heavy government intervention under both Hoover and even more Roosevelt). In the second with deflationary, it is idle resources that are the result, they get cheaper, and eventually leading to a boom. There aren't too many examples I am aware of of this though there is a train of thought that the late 1920s had inflation (to help the British with their war debt?) and then the Fed reversed course and starting deflating the money supply cause quite the shock. In any event, both are examples of problematic time periods during the price readjustment to the new value of money.
The main reason the government inflates money is so that they can spend without explicit taxing (inflation is an implicit tax for those that do not get the first rounds of the money printed) and allows for the wealth to borrow to acquire assets, where asset prices inflate with the money supply while the debt burden deflates with inflation. This is specifically to help rich people get much, much richer.
