> If the prosecutor so strongly feels that a weak case has a chance of getting a conviction

Who says that's the case? US courts are overloaded and public defenders are massively overloaded.

Most people can't afford to hire a good lawyer, and a (let's say) 10% chance of years in prison isn't worth gambling versus a plea deal to them. Prosecutors know this, file massive scary charges, and motivate people to settle regardless of innocence or guilt.