FWIW the "rule of law" is a reference to the idea that the law should be applied equally to everyone regardless of their position in society, and has nothing to do with the crime rate.

https://www.uscourts.gov/educational-resources/educational-a...

No. Catching murderers (for example) is a basic function of the justice system. Of course the US justice system does have many flaws and in some ways much worse lately, but compare with Somalia or Haiti and you'll see that there's quite a long way down. It could get much worse.