So, I know there's one particular high-profile federal investigation in the news these days. I know the people involved are total professionals and it's an important case to get the full facts on, but I'd like to ignore it, or say it's more of a window into larger federal investigation procedure – and I might recommend using a totally different case, perhaps this one about credit card fraud, if you want to imagine details of their work.
In particular, I'd like to (setting aside essentially everything else) very favorably compare federal investigators to local police in every jurisdiction I am aware of. In particular, I'd like to note how their actions demonstrate their appreciation of the distinction between guilt and belonging in prison (or even jail). In that credit card fraud investigation, it's clear they figured out the culprit almost instantly. All the hard work is in constructing the proof. Saying you hate criminals and will cross lines to put bad guys in jail isn't "tough on crime," it's "weak on capability". You want the bad guys to go to jail and stay there? Do it by the book, one step at a time, meticulously. That's how they do it in the majors.
Obviously, they still make mistakes, but fewer unforced mistakes, and dramatically fewer process mistakes (like unwarranted non-consent searches).
It's worth pointing out this is precisely the standard we should hold law enforcement to – making few unforced or process mistakes, being meticulous, and cautious in their actions, only making arrests when charges are not just imminent but also reasonably expected to be worth the court's time. When mistakes are made, they are (more) usually atoned for (than other law enforcement agencies).
And their status reflects that. As far as I can tell, the FBI handles many serial killer cases, not because of cross-jurisdictional necessity, but because they're really good. Presumably, there is also a budgetary/structural reason too (if you need a massive influx of money into one spot for a particular e.g. bombing, it's much easier to just have a floating team of experts who don't need unique appropriations). But at its core, they do the job of investigating crimes much better, and are seen as, not just more expert, but cooler.
This is probably how all of society should work. It should be cool to do an important job well. And as much as it's easy to talk about the bits of society we'd like to change, I think it's just as important to specifically recognize when society is basically doing something well right now. And I think we are, at least when it comes to this.