I would highlight this article on money creation in the modern economy (by researchers at the Bank of England) - (link to article). A key observation is that modern central banks do not directly determine the money supply, they set the rate of interest. (The policy of Quantitative Easing complicates matters, but what is happening there is that the monetary base is larger tha usual, but the central bank cannot set it below an effective minimum.)
This means that the central bank is not really determining "the money supply", but rather reacting to the private sector's demand for money at the target interest rate. In other words, the central bank has no ability to keep "the money supply" at a constant level. (The fact that the "money supply" is a vague term does not help. Is it M0?) It would have to move around the interest rate in a fairly erratic fashion in order to attempt to keep the money supply constant. (This was experienced during the money growth targeting experiments in the 1970s and 1980s.)
The money supply does not have stable short-term relationship to other economic variables. Even if it were possible to keep it constant, what objective would that achieve? Other variables would be moving around, in probably unwelcome directions. Instead, developed country central banks attempt to keep an economic variable that people care about - inflation - near a target level. (Other targets include fixing the price of the currency versus a foreign currency, or even gold.)
From a theoretical point of view, if money velocity were stable, nominal GDP would be stable if the money supply did not grow. Since we expect real GDP to grow as a result of productivity growth and population growth (in most countries), the implication is that there would be a steady deflation in the price level. This would imply that workers would need to get annual wage decreases, which is a situation that is psychologically unwelcome. As a result, there is a bias towards a positive rate of inflation. This implies growth in the money supply (assuming constant velocity).
A psychological bias against deflation is not just an arbitrary preference; in real-world data, wage decreases are avoided. (Sorry, I do not have a reference; I discuss references later.) Therefore, if policy attempts to force wage decreases, the result is that workers are laid of instead. Output would fall, that is, there would be a recession. This is a suboptimal outcome from almost any standpoint. An additional real-world issue is that debt contracts are entered into with the implicit assumption of positive earnings growth. Deflation leads to mass defaults, and recession.
There is a large literature on the optimal level of inflation, which was a hot topic when central banks entered into the inflation targeting. The reader should be able to find dozens of articles in this vein either with web searches or at the websites of inflation targeting central banks. I found this survey paper from the Bank of Canada published in 2015, which I assume would be authoritative (I have not read it). (Link to survey paper.)