Ok, without getting entangled in the semantics of burden, let's see your apparent solution. If "more attainable" or free (higher) education is the solution, then countries like India and China, among others, wouldn't have the poor and "undereducated," right? Or even European countries with free education wouldn't have the poor and undereducated. And yet...
I was listening to Jordon Peterson (and no, I don't agree with everything he says. I also listen to liberal podcasters too, lately Jonathan Haidt) and he made a rather interesting observation, which is somewhat depressing. But it could go a long way to explaining why we seem to always have a 15% poverty rate in this country regardless of how much money we spend.
He pointed out the US military has an extremely large range of jobs and range of skill set requirements for those jobs, not to mention a very large range of stress levels depending on the particular job. This range is so big in fact that it somewhat mirrors the range of skills in a normal economy. Now regardless of this huge range, the military has found that people with an IQ below 85 really cant fit in anywhere and are denied entry, which is about 10% of the population.
So the military operates with the policy that 10% of the population is too unintelligent to be useful regardless of the very large range in differing levels of job skills it has.
If you juxtapose this reasoning onto the overall economy, it could be the case that the 10 percentage points of that 15% poverty figure is due to 10% of the population just being too unintelligent to make it out of poverty. This is a pretty depressing theory, which could be true, and, if so, I cant even imagine how you would fix this. Although more education can certainly improve overall knowledge, your cognitive skills are pretty much set biologically, so I am not sure more education is really going to change anything.
The remaining 5 percentage points could be accounted for from people just entering the workforce and therefore not make a lot of money yet, or someone being hit with an accident that puts them in poverty, etc. Often though, these are temporary positions for most; it's just a large number of people tend to cycle in and out of these situations.