> should we simply ignore it and let the children turn out idiots as well?

Just because you're an idiot at 18 doesn't mean you are one for life.

> so that's why we designed schools that should compensate even for dumb parents.

Does that actually work?

> against the concept of putting all the responsabiliy of raising children onto the parents.

Then how do you feel about parents requiring a license before they have a child? If you wish to invite yourself into their responsibilities shouldn't you also invite yourself into their bedroom first?

> If you wish to invite yourself into their responsibilities shouldn't you also invite yourself into their bedroom first?

You're turning of question of measure (how much should society be involved in raising children) into an all or nothing debate, which I explicitly want to reject.

> Does that actually work?

Yes, because of mass education almost every adult you meet can read and write, something new for the last 100 years. Just because a system has (currently huge) faults, doesn't mean we should remove the system entirely.