Well, without a trial, how do you know they are guilty?
They admit guilt, because the punishment for the trumped up charges is so out of relation to the crime that happened for real. (Which does not mean that the defendant did the crime, or even a real crime happened, it's just the "visibile" thing) Now we've already concluded that many people take the plea deal to avoid that risk. (Hint: Because of minimum sentencing standards yet another safety valve has been disabled, e.g. the judge sentencing you for a dozen guilty counts to 40 hours social services, because he can see the real scope of the "crime").
So without that coerced admission of guilt how do you know that these guys are guilty? Just because the prosecutor (which risks nothing if he puts an innocent on death row, actually, getting the gulty verdicts even if they are turned over a decade later might be a career boost) says so?
One of the relevant outcomes of the American revolution was the right to a jury trial to avoid these kinds of abuses. The government has managed to void this right by putting an incredible high price (e.g. risk to spend your life in prison for something that might be a misdemeanour worth of a $500 fine. Or not even that.)
One last thing, yes, jury trials are a load for the system. But somebody is creating the load. Notice that many of these "small stuff" in most European countries would have been handled (as being dropped, converted to an "voluntary" reparation) much earlier, e.g. at the police level.
And before you cry, I live in big city, and I can walk the dog in the "worst" part of the city at night, don't carry, and the expected outcome is that I'll just get home, and the dog might be slightly tired. (Not the expected value for some US cities, where I was told by locals, no you cannot carry that expensive looking stuff in the subway). So while our mild justice system can be frustrating from time to time (because you often have the feeling that the perp is getting of easy), it seems to work better than the harsh system (walked the street with a red light, oops, it's 3rd strike, so it's mandatory life in prison).