In short ... the constitution of the US guarantees, under most circumstances, a trial by jury. A citizen also has Miranda rights (see Miranda v. Arizona). If 'you' cannot afford an attorney, one will be provided for you. That provision comes at the cost of the state. Furthermore, trials take time. Time is money.
If EVERY citizen who was arrested insisted on litigation (as opposed to arbitration or negotiation) - that would cost the state a lot of fucking $$. He thinks it would cost the state so much, they could not provide the trials. Because one has a constitutional right to this trial, if it cannot be provided in a reasonable time, then in fact, any charge would have to be dismissed. (Dismissed would mean on file with the courts BTW, so next time around, the charged you were never tried for would be in the records...fuck).
This idea is absolutely fucking absurd, because most of the people who commit petty, victimless crimes, are caught red handed and multiple trials, as we do now, would happen in a day, across all 50 states. Perhaps you have herd of a dash cam, and now there are body cams too. The defendant can't 'filibusterer' the courts by calling a million witnesses and just having them talk shit all day.
Worst, and he mentions this in the video, when you plea not guilty, and your found guilty (eventually you will be), expect to serve much more time, pay higher fines, etc. The court wants the money back they spent on that lawyer for you.
So (not that you do) if you want to be the person that was most likely caught red handed going to trial that's going to take bout a day, maybe two, getting the book thrown at em' in hopes that other people are raising their hands to be in your spot b/c "It'll shut the gov'nt dwn"... good luck to ya.