Extradition is generally thought of as when a person from country A who is convicted of a crime in A flees to country B, and country B then extradites said person to country A to serve out their sentence.
It's not meant to be a system to convict people incapable of defending themselves in a foreign court.
Plus, there are extradition treaties: countries A and B have to _agree_ to the conditions under which A will extradite to B and under which B will extradite to A.
> The proper process should be like this: if country A thinks that someone from country B has committed a crime against them then they should come to that country and prove it in a court without being able to add additional charges.
Courts in country B generally have close to zero understanding of the legal minutiae of country A. Ignoring jurisdiction questions, what you're suggesting is that courts in country B have to:
* understand the hierarchy of the legal system in A (what precedent is binding, what precedent is advisory),
* understand what is and isn't a law (e.g. if A is a common law jurisdiction and B is not),
* somehow reconcile legal procedures in A with legal procedures in B (e.g. when are you allowed to ask the judge to dismiss a case? what's an acceptable situation to ask for N more weeks for discovery? how much time is considered reasonable? who do you file paperwork with?)
* somehow decide what constitutes a qualified attorney (e.g. in the U.S., every state has its own qualification process for attorneys to practice in that state, so being admitted to the bar in Colorado doesn't mean you can practice in Florida, and this also extends to the federal govt)
and goodness knows what else.
In general it's good to assume that if there are millions of people in a given system, there are _reasons_ (not necessarily good ones, just plausible ones) the system works that way, particularly when it's a system you have zero understanding of.