Extradition isn't unique to the United States, though. It's a common feature of most large country's legal systems.
This doesn't mean that any country can prosecute foreign people with arbitrary laws at their leisure, though. Most extradition agreements would require that the offense be a crime in both countries, for example, and require a reasonable expectation that the punishment will be proportional to the crime (i.e. not petty political retribution).
In your US-Mexicon-Peru example, Mexico would indeed be likely to hand over the US citizen to Peru if (and only if) the accused criminal act was a crime in both countries. Mexico has additional constraints that would forbid the extradition if the death penalty was a likely outcome, but if the likely sentence was a prison term, the evidence was sufficient, and the crime was reasonably serious then the person would be on their way.
Ok but Anne Sacoolas ran over and killed a kid (definitely a crime here) and she wasn't extradited.
While Julian Assange exposed a US war crime and is extradited because US espionage law literally counts that as spying. Not a crime in the UK.
It really does appear that "at their leisure" is precisely how it works. There's the exercise of raw power with a thin veneer of false legal pretext on top designed to manufacture consent and convince those susceptible to the just world fallacy.
I have to admit though it would be interesting if the UK played a game of tit for tat here. We will extradite Assange, but only after you send us Sacoolas. But they probably won't because Assange being prosecuted is also in their national interest, whereas Sacoolas facing her charges has little bearing on UK national interests.
Sure. People whom the US doesn't give a fuck about.
"At their leisure" and "one rule for us; another for you" still applies. Sacoolas wasn't an exception in any meaningful sense. She is very much the rule.
The US cares about US operatives because they have a job to do on behalf of the US. The operatives can't do their job if the host nation holds the prosecution of their spouse over their head. I think you may be under the false impression that the United States is unique in this regard but it's basic diplomacy as standardized by the Vienna Conventions on Diplomatic Relations [1] - Article 37 specifically.
[1] https://en.wikipedia.org/wiki/Vienna_Convention_on_Diplomati...
It's conventional for the diplomatic immunity to be waived if an actual major crime took place as a gesture of good faith.
The fact that the US doesnt do it here demonstrates just how little respect it has for the UK.
I'm my opinion though, this just reinforces the idea that it didn't matter what the rules were - people in power were sufficiently motivated to justify what they wanted to do, they just needed a way to make it relatively palatable to the general public.
At least one UK court disagreed with your interpretation. AND the US and UK re-wrote the agreement after the incident, which strongly suggests the agreement did originally allow families to receive immunity.
The judge in this case, followed the rule of the extradition treaty law...
...but then again, ALL laws are rooted in the initial power politics that set them in motion.
What better time to slip Uncle Sam a favour?
The timelines of the extradition and the submarine deal don't match up exactly... but the idea that the English-speaking countries can rely on one another runs deep and long.
There were often such empires around the world. Rome for example.