> That's not possible because jaywalking has a maximum penalty, and the judge can't exceed that maximum penalty.

That's part of the point. The maximum penalty for many nonviolent offenses is absurd.

> One of the reasons we have so many felonies these days is because sentencing someone to jail for a single day on a misdemeanor offense for stealing a pack of gum for the 20th time can require a jury trial just as onerous as a felony offense with a 20 year sentence.

But why is this a problem? The purpose of the trial is to deter the other million people who would have committed petty crimes if they weren't prosecuted. It doesn't matter if the trial costs ten thousand times more than the value of the stolen goods. Moreover, if the sentence would actually be one day then guilty people would just plead guilty without coercive plea bargaining because it's less trouble to serve one day in jail than to waste two weeks of your life going through a trial and then serve one day in jail anyway.

Whereas if you're innocent you may very well be willing to spend two weeks at trial to clear your name, vs. the status quo where if you try to do that you'll be charged with a dozen vague offenses that everyone commits in the course of an ordinary day but are only charged against people who demand their day in court instead of accepting a plea for some other offense the prosecution isn't sure they can prove, all of which have coercively onerous penalties.