Living in Europe, I’ve observed how the federal ownership of law enforcement works, and won’t complain about it.
Cops all attend a minimum of one year of a police academy. Idiots won’t pass the exams or the physical fitness requirements to even enter the academy process. You end up with a fairly smart rookie, and a general career path. If you screw up....you get fired and will never work again....anywhere within the country.
Speeding ticket gimmicks via the cops? They run some minor operations but it’s mostly now a blitz-camera operation that cities put up.
Well your complaints about US locally controlled policing are mainly red herrings. There are a few bad cops and they get press especially here, but there are more bad TSA than bad local cops. There is good training in some localities and if you don't like the training in yours, you can advocate more or you can move.
Turning over all US cops to federal authority is an idea beyond bad. Imagine the BATF doing every domestic violence case. Imagine the IRS/FBI collecting local sales taxes from "tax evaders". Back in the bad old days there was federally run drug smuggling operation near me. There was just one local cop corrupted (that I know of), but that corruption came from above.
The reason the Europeans put up the Gestapo is the same reason they give in to most other forms of authority and will continue to do so until the next conflagration there.