Spent lots of time in public schools all over the country and overseas and I've seen both ends of the success spectrum.
I don't think the school needs to replace the family totally, but I do think the system needs to be updated to reflect today's reality. In Hawaii we had year round schools which meant you had a 1 week break in October, 4 weeks in Dec/Jan, 2 weeks in April and 6 weeks in June/July. Kids retained more and the longer holiday break reflected what a lot of workers experience. In Pa we have 10 weeks off in Summer, a week between Christmas and New Years, 4 days off in the Spring. Teachers love the long summer off, parents and kids suffer with it.
The biggest criticism I have with the American public education system is simply that the kids have very little time to focus on creative thinking and problem solving. In fact they have very little time to just sit and think and absolutely no time to assimilate anything they are supposed to be learning.
#2 is the unions, while necessary at one point, have become self-licking ice cream cones and made education more about the teachers, data, teaching techniques and student behavior--the students learning something is actually somewhere around 9th priority. Now, no teacher or administrator will agree with that and will point to the sacrifice they put in to teach the kids. But your priorities are shown by where you put your money and when I see a $100 million budget that has less than $50k for library books, $0 for new text books, and $50mill+ for teacher salaries and $500K for teachers to go to grad school it is clear where the priorities lay.
I would radically change the student's day by increasing physical fitness, music, art and other creative outlets as well as teach the core subjects in terms of pragmatic application. School would start with a physical component and finish with a quiet period where the kids could read classics, listen to music, write or simply sit and think. The day would be at least 8 hours so there would be enough time to focus on the subjects. It would also be somewhat self-paced so a kid who was reading or doing math at a higher level then others the same age could easily be challenged.
That's my rant for now.