I agree that a lot of people commit crimes in the U.S. because their basic human needs (including mental health resources) go unaddressed. The best way to reduce crime is making sure everyone has housing, education, employment, healthcare -- all the stuff any socialist state would do its best to guarantee.
But people without acute mental health issues also commit crimes, and not everyone who has an acute mental health issue will voluntarily engage in treatment. And even if a revolution won total victory tomorrow, society won't change overnight. I'm reading Justice in Moscow, by George Feifer. It was published in 1964 and written based on observations from Soviet courtrooms around that time. There were still "real crimes" committed there, as there are in China today.