The prosecutorial advantage is even bigger in grand juries (ie. the juries that decide whether the suspect will be charged or "indicted" with a crime), where only the prosecution's side is heard and the standard used to indict is much lower than the "beyond a reasonable doubt" standard used in a real trial. The running joke being that a good prosecutor could indict a ham sandwich.
It's after indictment but before trial that the prosecution pressures the defendant to take a plea deal (ie. plead guilty to reduced charges) to avoid risking going to jail for a much longer time and bearing the insane expenses of a trial.
To my memory, in the US only something like 6% of indictments actually go to trial, where (as you point out) the prosecutors have a huge advantage. 94% of the time inicted defendants plead guilty and never actually get a trial. In some cases, like with Aaron Swartz, they commit suicide.
So for the overwhelming majority of cases, it's not what happens at trial that matters (as they never get a trial), but rather what happens in the even more skewed for prosecutorial advantage grand jury that matters -- a grand jury where defendants and defense attorneys are not even present and where their side is not heard.