[0] https://www.nacdl.org/reports/misdemeanor/ page 21
[1] https://www.bja.gov/Publications/PleaBargainingResearchSumma... page 1
But aren't those statistics based on a system that's incentivized for them to be guilty? That's like trusting an environmental study funded by an oil company.
That aside, you're assuming that because most criminals (that get caught) are stupid, that most people accused of crimes must be guilty. What if we consider an alternative theory - the police are stupid? Is that any less likely than criminals being stupid? Another possibility - the police don't care and just want to meet their numbers. And another possibility - people have underlying prejudices which they use to justify their actions.
In order to reach your conclusion you need to make a lot of assumptions, for which you provide no evidence.
It's a critically vital function in preserving the rule of law.