A series of answers were proposed to similar questions in the world building forum.
The relationship to plea bargaining is as follows:
When the prosecution has a strong case with a high probability of winning, it insists on going to trial and will make only slight concessions relative to the result that could be obtained at trial.
When the prosecution has a case of typical strength with an intermediate chance of winning, it will normally make a significant concession in the severity of the offense charged or other agreements that impact the length of the sentence, relative to the result that would be obtained if the prosecution fully prevails at trial, rather than "roll the dice" and usually the defense will agree in exchange for a more lenient sentence.
When the prosecution has a case that is weak (but being ethical, believes that there is probable cause to support), it will normally make very deep concessions such as agreeing to a much less severe charge or for example to probation or a deferred judgment, to at least impose some punishment, in order to avoid going to trial, even when the potential punishment if the prosecution full prevails is very high.
Plea bargaining rates in the federal system are in the mid- to high 90%s, while plea bargaining rates in state systems are often in the 70% to 90% range (federal prosecutors can leave weaker cases to state prosecutors if they want to and have a stiff hammer due to high mandatory minimum sentences for many offenses and the sentencing guidelines, but state and local prosecutors have to take what their less elite law enforcement officers come up with). At trial, prosecutors typically win convictions well over 50% of the time (although not too much more, because the more clear cases are either dismissed by prosecutors as unproveable prior to trial or are plea bargained).
The net effect of the current system is that the severity of the sentence imposed in the vast majority of cases is proportional to the probability of the prosecution prevailing at trial times the likely sentence if it does prevail, as evaluated mutually by the prosecution and the defense. When there is not a sufficient consensus on the fair sentence in light of those factors the rare trial happens (and more often than not the defense rather than the prosecution overestimates its chances).
Unfortunately, this also means that the biggest penalties for going to trial are in the weakest cases in which the prosecution just barely manages to convince the jury and there is a strong probability that the defendant is actually innocent, as opposed to the cases where it is fairly clear that the defendant is guilty. And, people who are actually innocent of everything are most likely to roll the dice and go to trial, since people who are guilty of something know that in any fair resolution that are going to face the significant downsides of having any criminal conviction on their record, while people who are actually innocent may reasonably (although sometimes inaccurately) believe that the system will protect them and allow them to escape all consequences except the costs of defending themselves in court (if they can afford it).
Another option that prosecutors have in a case where proof beyond a reasonable doubt may be difficult or impossible, is to bring a civil lawsuit or to seek an administrative penalty, which may result in loss of a licenses or payment of a fine or compensation, rather than bringing criminal charges. In these cases, the prosecution only has to prove a case by a preponderance of the evidence in most cases, and usually, the defendant has no right to an attorney at public expense even if the defendant is indigent. These fines (or civil forfeitures) can also help fund the criminal justice system that pays prosecutors and other participants in the process.
Below that standard, prosecutors can seek search warrants, wire taps and arrest warrants in cases where there is merely probable cause to believe that a person committed a crime, which in addition to setting up future prosecutions can also be used as a form of punishment/harassment of someone prosecutors believe to be guilty of a crime even though they may not even have the evidence necessary to prove a civil suit, but the amount of impact that a search warrant, wire tap, or arrest can have on a suspect is much less than a full blowed prosecution.