The problem is, with most things in Life, you do get what you pay for. Nothing in this world is ever truly free. There's always a cost. (Sometimes it's not so obvious. Sometimes it's not money.) But with Public School systems? Oh, absolutely! Private schools will attract the best and brightest teachers, because they can easily afford to pay for the best. Public schools tend to attract individuals who became teachers for the insane level of job-security. Basically all the wrong reasons!
When you get teachers like that, it's no wonder students aren't motivated to learn. I attended public school. I remember Mr. Perez, and Mr. Poumari. I remember them because they were very strict, very motivated to teach, and very much cared about their students. But rarely openly showed it. I remember two other teachers' names. But only because they were so miserably incompetent as teachers that they crossed the line into being comically bad. (One of whom was an Asian Spanish teacher, and she could barely speak more than five words of English.) I'm seriously not even joking!
But those two men could have easily worked at a Private school for significantly more money. But chose not to. They chose to stay and motivate their students at Flushing High School back in the early 1990s. Problem is you have two teachers in a massive Public school. The number of students they can reach and motivate is extremely limited.
Compare that to some of the mental midgets we had as teachers. One of whom once went on a half-hour tirade that "None of you matter. None of you will make a difference in this world." What did he expect us to do, cure Cancer? Mr. Motivational Speaker also once bragged how he literally dehydrated himself during a vacation with his two sons in Egypt. They were desperately looking for more water, while he stood around feeling smug and oh so clever. Didn't even try to help his own two sons. Shows you what kind of man he was. And, what type of teacher. When someone like that is the Standard, no wonder kids aren't motivated to learn. Doesn't help that so many parents have no clue, nor desire to actually parent their children. When someone isn't raised right, you can't expect them to do right.