Thats not how it works or what happened.
You can only be given a sentence for the crime you have been convicted of, otherwise you could easily appeal.
> Is this reasonable? Should we be satisfied with how this works and not want to change anything about it?
It doesn't work like that, and I wouldn't be satisfied by a court system that does work like that. It'd fucking disastrous. If anyone convinces you that it does work like that, they are either a scammer, or want to make the law system _very_ scary.
https://en.wikipedia.org/wiki/Habeas_corpus_in_the_United_St... which have been there for _many_ years. Its a common law principle that at least twice as old as the USA.
> You can only be given a sentence for the crime you have been convicted of, otherwise you could easily appeal.
If you're convicted of a crime, let's say selling drugs, that carries a penalty of up to life in prison even though most people get 5-10 years, and then you're sentenced to life in prison after the person doing the sentencing is prejudiced by these murder allegations you've never been convicted of, what's your basis for appeal?