Plea bargaining in the sense you see on TV - "plead guity to the jaywalking or we seek the death penalty" - is, to my mind, coercion. I don't know to what extent that exists in reality, however.
In reality, fewer than 10% of criminal cases go to trial. Fewer than 2% of federal criminal cases go to trial. Mandatory minimum sentences run in the multiple decades, making a bid for a trial an extremely risky proposition. This is extortion, plain and simple.
It's in nobody's interest to spend public money trying someone who is willing to plead guilty
Only if you assume that he is actually guilty, and not an innocent person assuming that he's going to be railroaded at trial, and taking the only chance he sees to minimize the damage.
that has to be balanced against the very large cost and time savings.
If it's not worth paying for a trial, it's not worth prosecuting at all. If you can't afford to offer your citizens trials, the solution isn't to shovel people into prisons until you have the largest prison population in the world(which we do, and it's not saving us any money either). The solution is to reexamine your laws, figure out the ones that are worth having, and which ones you can't afford.
A real justice system doesn't cost us money, it saves us money. e.g. if we stopped prosecuting murders, chaos would ensue, and we would stop having a functioning economy. That would cost us a lot more than it would to prosecute murders. If we stopped prosecuting drunken driving, carnage on the highways would discourage people from using it, damaging our economy. Again that would cost us more than DUI enforcement. And that's just considering economic damage, and not the human costs.
So all this talk about cost saving is quite frankly bullshit. If the laws you are enforcing aren't paying for themselves, directly or indirectly, it's a bad law. Trying to save money on top of the inherent payoff of justice by denying us our rights is incredibly wrongheaded.