> That's also the reason why the US has almost 25% of the world's prison population
No it's not. The US has the world's highest prison population for two reasons you didn't list. 1) repeat offense violent crime in inner cities, which is what the majority of inmates are in for. 2) The war on drugs, which is directly and indirectly responsible for most of the crime in the first reference, to go along with the substantial prison population that is there for only drug offenses. There have been numerous studies done on the US prison population and it does not mostly consist of people in there on trumped up charges and wildly exaggerated sentences (and yes that does exist very obviously), it mostly consists of repeat violent offenders.
> with a growing tendency
Shrinking tendency in fact. The total US prison population peaked several years ago and is now declining and is set to decline dramatically over the next two decades as the war on drugs is ending. If your theory were correct, the US prison population would still be spiraling upwards at the old rate.