> But the objection you are describing is the difference between a possible, usually highly unlikely maximum sentence and a sentence arrived at in a plea deal. Only one of those is a real thing, though.

The maximum penalty does actually happen though, it's just not common. The problem is that you don't know if it will happen to you before the trial, so its existence is extremely coercive. It scares the crap out of people -- and people are risk averse. They'll take a 100% chance of 2 years over a 1% chance of 30 years, even if the expected value is lower, because on the off chance the coin comes up tails six times in a row, they lose their entire life.