Your argument with each other is a distraction. The point you are arguing about is the behaviour of people in particular, but my OP is about the overall situation averaged at a country level. Try to stick to the topic, please.
M4 isnt just $$ in cash - its all monetary instruments. If you look at 'real estate' (property) prices, they track GDP growth/ M4 growth rather well, demonstrating that the 'value' of property is largely fixed in 'real' terms by that ratio, at least in the UK.
As I see it the concept is rather simple. if GDP increases so there is more stuff created/purchased/used , and if no money is 'printed', then then prices must fall to accommodate the 'purchase' of the extra product. For money to represent 'value', then the money supply must expand to cover the increased GDP so each $ or £ can buy the same amount of stuff. When balanced there is no inflation as the value stays fixed.
Governments who operate the banking system's supply of money try to manage the supply to keep a fixed inflationary pressure as its to their advantage. They do this by 'printing' more money than required by GDP growth. The result is an 8 fold decrease in 'value' (in the UK) of the currency since about 1984.
The key thing is that Value isn't Price. Government inflation figures demonstrate this admirably where the 'basket' contains things that are getting cheaper, mostly due to technological reasons. But the real value of money is reflected in the more broad cost of living (including housing) and of doing business.