Study after study seem to indicate that suplimentary Hebrew schools are a failure. Some studies have even shown that Hebrew school is more likely to turn a child away from Judaism than towards Judaism.
The blame cannot be placed on the valiant professionals who run these schools. Many of them are talented educators with innovative ideas and they are doing the absolute best that they can, but they are fighting an uphill battle. By the time the students get to Hebrew school after a long and hard day of regular school they are exhausted and in no condition to learn. Not to mention that they are only there once a week and there are no real consequences for misbehavior.
And those handicaps only apply to the kids who actually show up. Today Hebrew school is more irrelevant then it ever was. Kids are more over programmed then ever. The best kids are also involved in serious after school activities that give them the opportunity to engage in something they are passionate about and in many cases even give them opportunities to travel and compete or perform all over the country.
In addition, the parents of these kids are products of hebrew school themselves. In past generations parents made hebrew school a non-negotiable and kids were forced to go. Today the parents are more likely to encourage other activities that conflict with Hebrew school.
The reason day schools are mostly successful is because in a day school being Jewish is incidental. Very few kids in day school attend suplimentary jewish programs in the evening. After school they are free to be teenagers and participate in whatever they want to.
Hebrew school is an extra curricular that most Jewish kids are not interested in. There are those few kids who actually click with Judaism and want to make Hebrew school their primary activity. Those kids go on to be very active in their youth movements and eventually decide that they want to be Jewish professionals, and sometimes Rabbis.
The Jewish world has already decided that there must be an alternative model to Hebrew school to give Jewish kids a sense of Judaism. But in the meantime, I do not think that Hebrew schools should be stopped altogether. They are still the best breeding ground for the Rabbis of tomorrow and one of them may one day discover the solution.