Every kid does have a pencil. Judging from stories my mother and mother-in-law tell (both public school teachers, one in the inner city), the teachers have to provide one for them because the kids have not been taught how to remember to bring them and they have no ability to punish them for forgetting them.
My mother-in-law literally hands out a bag of 10 mechanical pencils at the start of the semester to each student, which she pays for herself. A week later these kids are asking her if they can have a pencil.
Again, the issue is discipline and motivation. The kids have zero incentive to remember to bring a pencil, and zero consequences if they forget. If anything, they're being taught that you don't have to be responsible: the teacher will bail you out anyway and can't impose consequences if you don't remember.
These kids, even in low-income areas, go to school in palaces. These buildings get so much funding from states, federal government, and the Department of Education that they often abandon perfectly useable buildings to build brand new ones to the tune of tens of millions of dollars. Your comment about asbestos is a complete strawman.
You want to make a kid feel hopeless? Put him in a 45-minute math class where the teacher has to spend the first 15 minutes of class dealing with three troublemakers who are so disruptive they have to be sent to the office multiple times a week. The kids in that classroom will quickly internalize the idea that education doesn't matter, discipline doesn't matter, that they themselves don't matter.
That's what's driving the hopelessness you describe. Multiply that by 180 days a year, 12 grade levels, and yeah, you'll get the negative synergistic spiral you described in another comment.
If kids don't learn discipline at home, and don't learn a modicum of it at school, well, you get crime. Not a year goes by where my mother-in-law doesn't see the mug shot of one of her students from 10 years ago on the nightly news. It shouldn't be surprising to anyone that after living 18 years without any real consequences for their behavior, these kids get out of school and sometimes turn into criminals.
Teachers can't even teach in many of these schools. They spend more than half of their time writing up troublemakers for the nth time this semester and leaving voice messages on their absentee father's phone. Who wants to sign up to be a teacher in that environment? The exodus of teachers from the public schools proves my point.
You want to give those kids hope? Discipline them. Kick the troublemakers out of school if they continue to misbehave. Show them that they matter enough to properly educate and train. Not just reading, writing, and arithmetic, but the basics of society: some behavior is not okay and will not be tolerated, things are expected of you, and their are real and sometimes painful consequences for not meeting those expectations.
Do that and you'll see something crazy happen: those kids will start learning, behaving, and growing into productive, honest, good citizens. Most of the problems you describe will disappear. Until we do, expect more of the same.