1. Minimum plea bargain cannot be less than half of maximum? What about crimes where the sentencing guidelines are already spanning 2x? That would mean you could get a lighter sentence by going to trial than the minimum plea.
Of course you can get a lighter sentence by going to trial - by being acquitted.
And no, it would not work that way, because if you had an open and shut case with a plausible sentence of 20 years, prosecutors wouldn't or at least shouldn't be offering plea bargains of under 10 years.
I saw an argument recently, that most of the problem has been caused by the fact that sentencing has been pulled out of the hands of the judiciary (though mandatory minimums etc). Judicial discretion in sentencing was once a check on this sort of thing.