You can't define inflation as you want. Inflation is an government official indicator with a very clear meaning.
You can; whether that's useful or not depends on the definition and context of use.
> Inflation is an government official indicator with a very clear meaning.
No, its not. Inflation is a broad concept (well, actually, a set of different and interrelated broad concepts) with a number of different official government measures. The most common US government measure of price inflation, the most common kind people talk about, is the all items CPI-U (Consumer Price Index for All Urban Consumers.) But there are lots of other inflation measures, including official government ones used for important purposes, like the CPI-W (Consumer Price Index for Urban Wage Earners and Clerical Workers) which is used as the basis for Social Security COLAs. And also frequently cited is the CPI-U for all items excluding food and energy. There are also CPIs for other populations, CPIs for other categories of goods and services, PPIs (Producer Price Indexes), ECI (Employment Cost Index), and others. All of these are official government price inflation measures.
There are also official government measures of money supply, which equivalently are measures of monetary inflation. And there are a whole bunch of those, not just one.
My point doesn't depend on this tho, measuring inflation by rising prices isn't ideal, because you will be measuring multiple things at once, and only the people lose in that case.
Prices can rise and fall for multiple reasons, and knowing why helps to fix it.
If the price goes up because of a shortage, the increase in price helps stimulate more production.
Governments get the advantage of being able to inflate the money supply to the point were it prevents prices from falling, ensuring easier reelection at the price of the people paying more for things and effectively taxing savers.
Monetary inflation is one thing denoted by the word "inflation", and perhaps it used to be the more common use in general conversation. Its not anymore, price inflation, particularly consumer price inflation is the most common general use.
> measuring inflation by rising prices isn't ideal
It certainly is if you are doing for a purpose to which price levels are most directly relevant, which is quite commonly the case. There's nothing mystical about the word "inflation" that creates an all-purpose best measure (and, in fact, "inflation" is a name for lots of different things, which have complex interrelationships.)
Governments have the fiscal capacity to keep the economy going. Is your theory that, for instance, the USA economy would be better without the government stimulus?
When the economy goes bananas, if it's not sustained by the government, not only will be suffering of a big part of the population but the destruction of physical capacity and knowledge in the economy.
This is not the 19th century, that idea that the economy on its own works perfectly should be debunked by now.
Suppose the government defined "eastern time zone" to be a geographical area. And you live in western indiana, and commute to work in chicago.
Suppose the government defined "torture" to not include "waterboarding".