For one thing, at 18 kids can choose what they want to do.
At 18, you hope that you have raised your child to make good choices in life. You have basically done your job. If you have done it well, then they should be able to handle the pressures of college life.
Plus, in college kids are there that want to be. Most of them are fairly academic. No one is forced to go to college. No ones is going to be truant. Public elementary and secondary schools are full of kids that do not want to be there or shouldn't be there.
Colleges have a lot to offer that parents cannot afford: good libraries, science labs, computers, etc.
Most importantly colleges offer diplomas that most companies require to get a good job.
And schools don't? Honestly, most of the responses I get from homeschooling parents on FR is that the only public school choice they have is somewhere in the inner city ghetto when the TRUTH is that they are all in the upper-socio-economic strata and live in neighborhoods with good public schools...as well they could well afford private schools if they did not choose the public school option.