We really shouldn't care about what a 13 year old thinks they should be learning.
Of course, you can't let 13 year olds teach themselves, because they don't know what's out there and they don't know the best way to spend their time. But that's not the same as not allowing them to do things that they're interested in. Incidentally, I don't think that we shouldn't have any sort of required education, just that they should be a small part of the whole educational experience.
Being motivated by nothing means students will not learn or retain knowledge.
So yeah, I think letting a bunch of 13 year olds play video games all day would actually provide better results than keeping them locked up an a pseudo-prison like environment teaching them things that they're not interested in learning and for the most part wouldn't need to know anyway.
On the other hand, I don't really remember being taught many professional skills in school, and in any case, it's still practically unfathomable to me that kids could make it through 13 years of any kind of education at all and not end up literate and numerate.
Also, we spend a lot, however it's extremely unevenly distributed making it much more likely the scenario we're discussing comes about (someone making it through school without a useful education).