You are operating on the principle that finding the truth is the purpose of an interrogation. This belief may be false.

I'd also recommend watching this quite famous talk about the topic: https://www.youtube.com/watch?v=d-7o9xYp7eE

Well worth the time.

EDIT: Seems I wasn't the first to make that recommendation: https://news.ycombinator.com/item?id=26608636 ;)

It’s not. The purpose of interrogation is for the officer to gather evidence pointing to your guilt which will be presented at trial.

The trial is about figuring out the truth.

> The trial is about figuring out the truth.

Even that is an assumption.

I'm thinking about trials more as tools for the people in the legal system to advance their careers (unfortunately. I don't work there)

Fair, but as a defendant the trial is pretty much your only chance to tell your side of the story to the people whose decision actually matters. Police officers and prosecutors don't decide whether you go to jail so there's never a point to trying to prove your innocence to them.