But that is how the plea system operates. That is why the sentences are so long.
If the maximum penalty approximated what people are actually sentenced to, the prosecutor would have less leverage in plea bargaining and a much higher percentage of people would go to trial. Or the pleas would have to be more generous which would under-punish actually-guilty people who take the plea -- and reintroduce the incentive for innocent people to plead guilty.
The only way to get rid of that incentive is to get rid of plea bargaining. (Which would then allow maximum sentences to be much lower.)
Sure, if the plea system disappeared tomorrow, then initially sentences would probably be universally high. But at least wrongly convicted innocents wouldn't be treated more harshly than the guilty.
In time, different (probably mainly political) forces would bring down sentences to what society considers acceptable (two years in our example). Even if sentences didn't go down, at least they'd be aligned with society accepts for both guilty and wrongly convicted innocents. In any case, the absolute length of sentences is outside the scope of my argument.
Objecting to one criminal justice reform because it might exacerbate how the criminal justice system is also completely unfair in another, equally terrible way isn't very convincing, when you could actually be advocating to eliminate both problems.
And hey, no more innocent people railroaded into guilty pleas like they are under the current system. https://www.nybooks.com/articles/2014/11/20/why-innocent-peo...
Quite the opposite (in terms of pleas and cash bail). See https://en.wikipedia.org/wiki/Bail and https://en.wikipedia.org/wiki/Plea_bargain.
For example in England plea bargains are based on timing of plea only and are limited to one third off the sentence only. Bail is given by default and a cash bond is not required.
> Which country would you say does it right?
I'm not sure I'm qualified to say that some country does it right, but England for example is quite the opposite of the US in terms of "presumption of innocence" really having a meaning. The system hasn't ground to a halt, yet innocent people don't rot in jail awaiting trial just because they're poor, and don't have to plead guilty for fear of getting a 10x sentence.
The rest of your post just goes back to my previous comment about max sentences. If we reduce the max sentence for that hypothetical crime from 20 years to 3 years, then our system would be the same in that people who plead guilty would receive two thirds the sentence that those found guilty at trial.
Also, one of the reasons that the UK is able to handle this increased case workload (although a majority of cases are still plead down) is they spend a relatively high amount per capita when compared with other countries. Once again, I am not against a holistic change that reforms the whole justice system. But doing away with the plea system doesn't have the benefits that you suggest and has various downsides that you are skipping over.