The point is: (as dragonwriter mentioned), the student rarely makes this decision. Furthermore, even when the student does, or when the parents of the students do, the decisions that are being made are pretty heftily influenced by advertising, gut instinct, and in-general wrong thinking about education. Take, for example, the weird and broad anti-common-core movement. Parents don't want their kids thinking about mathematics, they want their kids memorizing math facts just like they did when they were in school. Parents are swayed by images of tons of technology being used in these charters, when it turns out that most schools don't use tech all that effectively (they just reproduce old behaviorist models of instruction in an attempt to automatize teaching - recreate the teaching machine as Audrey Watters puts it).
In fact, the recent OECD report about use of technology in classrooms around the world was just making news earlier this week: in schools where there's a lot of 1:1 use of computers, students actually fare more poorly. This isn't surprising to me, or anyone else who studies education and the school systems, because of the point above: those computers aren't being used to improve or extend interactive learning, they're being used to deliver memorization-based, fact-and-repeat instruction. That's the same kind of boring teaching that turned off generations of kids in the past, and we're reproducing it again in classrooms with computers. However, those classrooms are shiny, filled with young, idealistic, often very poorly-prepared teachers and are very photogenic to parents.
Even worse- the charter movement (broadly speaking) has subverted most of the assessment process by ensuring that what is tested is the most flat, boring, and fact-based material around. (This is, incidentally, my own objection to common core- not the standards, but the terribad implementation of those standards in untested and regressive assessments). The assessments are bad, tend to not measure good learning, and instead measure a student's ability to memorize and repeat factual information. When charter schools do well on that front, and when the pro-charter movement gets the entire narrative framed in terms of "bloated, failing public schools", it is not surprising that parents (and grandparents, and students, and so on) are generally mislead by this narrative. It's not surprising that people choose charter schools.
People choose to give their money to University of Phoenix, which is objectively a terrible idea. Marketing works. Shiny pictures of happy kids with laptops learning the basics works to motivate people. The truth is, good education is complex - not even complicated, but complex - and asking the general public to really grok the nuances of it is difficult, especially since everyone has their own experience of what worked for them and things were good enough for me when I was in school, darn it.
A brief aside: there are plenty of good charter schools and charter networks, which are striving to bring high-quality reform-oriented education to everyone, especially underserved minorities. However, these charters aren't the ones I'm talking about. There are plenty more that take district dollars and provide sub-par education, and somehow manage to keep either getting renewed or just change names every three years when they come up for re-accreditation. There's also plenty of poorly-performing public schools and districts. Teachers' Unions aren't a panacea.
Ultimately, the problem from top to bottom is that our school system is in the hands of people who don't actually know much about education. Many board of education positions (especially state levels, which exert a lot of control) are political appointments or elected positions. How many times do you read about stupid stuff some board of ed is doing - rewriting history or requiring creationism or other crapola? Education is complex and nuanced, and people seem to engage in the discussion thinking that there's a Simple Fix for everything.
Charters are just vouchers in disguise, and vouchers are just saying "let the Free Market fix it", because the Free Market is super-great at fixing things like the banking, energy, health care, and housing systems in the US. Other charters have "let's let Technology fix it" ideas or "we're super-rigorous, require dress codes, and provide Discipline by calling all our students Mr. and Miss Lastname instead of having real relationships with our students". There's dozens of silly simple fixes floating around.
And you want parents to navigate all of this? It may be arrogant of me to say it, but I honestly don't think most parents can parse through all the crap. Again, people are still paying money to University of Phoenix, people buy guns thinking it will make them safer, and do dozens of other things that are just plain foolish because people aren't experts in everything. If you could assume that someone had enough understanding of how people learn (at least having read the book... How People Learn, which is still a great primer), you could maybe assume they're going to make good decisions. But this is a decision that (as you point out) will stick with the kid for 13 years proximally, and influence their opportunities for the rest of their life.
We should regulate this market.