Not true, if money supply does not grow with population or economic growth it will be deflationary aka not stable. If deflation continues then people will hold onto money rather than buy things with it since things become relatively cheaper every day, which leads to economic downturn.
Is that a bad thing? Items would become more durable, planned obsolescence for products would all but disappear. Things would need to last a long time otherwise people won't spend on it. It would be good for landfills, fewer electronics and plastic garbage. I think it's sad that people in 2020s aftaid to hold savings because they know if they don't spend it, their buying power is reduced tomorrow.
> A stable currency would have an inflation rate of 0%
Sure, and if the government had centralized control of all prices, it could mandate that. Since it doesn't (even those that assert that power don't have it in practice), what it seeks to do, as far as stability, is try to acheive low short-term price volatility, and as it turns out, experience shows that low-to-moderate inflation helps with that.
The M1 [0] tracks physical currency in the economy. It would appear there is a rather large amount of literal money printing afoot. So while a sharp turn to dictatorship could stabilise the currency, there are probably less extreme measures the US government could take to keep inflation at 0%. 75% of (physical, not the important ones in bank accounts) dollars literally appeared after 2016.
The M1 isn't the measure that matters - but it is a fact that large amounts of money are appearing from somewhere and that is probably the most significant factor in the currency losing value. Price controls are an overreaction, there are easier ways to make the currency more stable.
A stable currency would have a stable Velocity. This is something both USD(which is inflationary) and BTC(which is deflationary) get wrong. We need a flationary currency.
A stable currency would have an inflation rate of 0%. Inflation does not cause currency stability, it decreases the value of the currency.
By definition, its value is changing.