I'm not quite sure I understand the divergence. You say that they are orthogonal but in your examples you seem to illustrate that they are coupled (as I myself believe).
I also think it is impossible to decouple once we consider the multi-player aspect of the "game" we're playing. Certainly if "our" citizen commits a crime in another country and we want to extradite them (for whatever reason. Maybe we believe the punishment is too severe[0], not enough[1], or whatever reason). Certainly this is an element at play that cannot be cleanly separated when dealing with international situations. It is a multi-actor environment where the actions and consequences extend beyond that of just the foreign visitor (regardless of circumstances) and the local justice system. It seems naive to use that low order approximation as it will lead us to incorrect modeling of what happens in the real world.
> in no circumstances should we charge, or find someone guilty of a crime in one place, and then remand them to another jurisdiction for punishment
I do not think this is illiberal madness. Quite the opposite! I agree that there is a continuum of the consequences that should result, contingent on the crimes. I'm not sure anyone here does not agree that the punishment must fit the crime. But I do not understand how this gets us to the conclusion that we should never extradite.
Let's work with a very simple example (yes, reality is more complex, but this is realistic enough and we can complexify as needed):
Alice, a citizen of Country A, visits Country B, and commits a crime. Alice is tried in Country B and convicted. Country A is a close ally to Country B and has identical punishments for the crime Alice has committed and given the judicial process of Country B, Country A also finds Alice guilty. She will receive identical sentencing. Country A request that Alice be extradited.
It makes perfect sense here to extradite Alice back to her home country. As I see it, there are some rather obvious reasons to extradite.
1) It builds and maintains good relationships between the countries.
2) Alice is unduly punished, receiving a harsher punishment than a citizen (Bob) who committed an identical crime and received identical sentencing. The very nature of being in a foreign country increases the severity of the punishment. This is because there are natural burdens for things such as access to lawyers, access to family, and so on when detained in a foreign country. These burdens do not exist for Bob. Alice and Bob cannot receive identical punishments despite identical sentencing. This creates an unequal and unjust system!
3) What does Alice's home country do?
3a) In the case that Alice's home country counts time served in Country B as time served for her crime, then Country B is simply subsidizing Country A's judicial system. That doesn't seem like a good outcome. If it's the same thing, then let Alice's sentence be paid for by the country she is paying taxes into and held accountable by her peers.
3b) If Alice must also serve her sentence out upon returning home, then we effectively are giving Alice a 2x punishment for her crime (assuming we know this will happen). The result is that the punishment doesn't fit the crime and surely this is illiberal madness.
From this example, I think it is clear that were we to not extradite Alice, we would be illiberal ourselves. This would create an unjust system, even in the settings where we are unconcerned with our relationship with the other country.
Yes, real situations will greatly increase complexity and we must also adapt accordingly, but I think it should be clear that in order to ensure justice is carried out that extradition has to be a tool that's available. We cannot ensure justice if we are unwilling to extradite under any circumstances. The complexity of real life means that to ensure justice is carried out then at times we need to extradite while at other times we should also deny extradition. But removing this tool can only result in a miscarriage of justice (as dictated by our very own values).
[0] e.g. US woman is imprisoned in Iran for not correctly wearing a hijab.
[1] e.g. US citizen violated US law but not local laws. Countries do extradite for this reason all the time.