YOU may have been perfect, motivated, willing to learn, and may have been given the opportunity to learn even if it wasn't mandatory. Many others would not, many parents wouldn't bother.
There's nothing fundamentally wrong with those kids, they just need a different direction and a little more support.
I don't know the system in the US very well. Kids can go to different sorts of colleges post-16 here in the UK, or could (until recently, this may have changed) opt out at that age and enter the workforce.
For ones wanting to learn, just don't force them to do so. OK, is someone is not much willing to learn - well, then it may be good to force to do so. But don't force everyone because some need it.
(It seems that forcing people to learn is very inefficient. And I think for that reason many times school are places to socialize, bully and drink doing not much work that it is necessary to survive... and not much places actually good for learning anything.)
And how do we get kids who could use it, but from backgrounds that wouldn't bother to educate them at all, into the system?
Mandatory education is a good thing.
As you know, daycare (and, say, crime and accident prevention), training, and cultural/national upbringing are different things, and they work differently, often with contradicting goals and methodologies. Currently we tend to treat "education" as a one thing, but in isn't.
I am all for all kids going to school (unless one can provide a better education), otherwise there would be a disaster of crime and poverty, much alike the one during the industrial revolution. However, what happens inside is extremely far from things which "make sense" both for them, and the society.
I just don't think that abolishing mandatory education/training/socialisation/what-the-hell-ever is a good idea, and it seems you don't either :)
[citation needed]
...and on the other hand putting smart kids _willing_ to learn in an uninspiring and oppressive environment. (Bad for their learning and devastating for their still developing personality.)
IMHO it's hard to find a worse crime against natural curiosity and willingness than _forcing_ people to do something.