Looking back I don't see that the OP mentioned the other big issue with plea bargaining: when innocent people plead guilty because it's often the best choice. My bad for adding my own context onto it.
Decent writeup:
http://www.nybooks.com/articles/2014/11/20/why-innocent-peop...
tl;dr: the current system incentivizes defendants (especially poor ones) to plead guilty regardless of innocence. This is caused by a combination of prosecutors/judges trying to be "tough on crime", overloaded public defenders, excessive bail, mandatory minimums and several other things.
I don't think plea bargaining is absolutely unfixable or evil but I also don't think it's a well-functioning part of the system as-is. I believe this is one of those cases where removing an option might be better for the justice system as a whole.