I think the confusion is that educating everyone together doesn't mean 'in the same class all the time'. You are all in the same school. Mix for some subjects, stream for others.
The more able students raising up the less able isn't literally the more capable kids helping to teach. It's being able to see your peers in your year achieving, giving you motivation to move up the sets in an environment where it's possible for you to do the same. It also enables those more academic but perhaps less practical individuals to see their peers with more ability in those areas achieving.
When children are able to mix in the playground, in PE, for some lessons, they are spending time with others with different abilities and maybe learning that they aren't a different species. As opposed to cutting children off entirely from children who achieve better academically. Because children who do better in class aren't always simply brighter than others.
Children whose parents can't, or won't, model some of the discipline academic achievement takes can learn that from interacting with their peers who do have those skills. For example, Joe plays with John at break. They are in the same class for registration. Become best friends. Joe isn't in the same set as John, but he would like to be, because they are friends. He's stimulated to get to John's level so they can be in maths class together. Maybe Joe never gets there, but he does improve more than he would have if he never got the chance to meet John at all. John, meanwhile, gets to learn that not everyone has parents who help with homework, and Joe knows useful stuff like how to fix a puncture. So John learns from Joe.
The idea never was to just bung them all together in all lessons, it was to put them all together under one roof with the same opportunities to access higher levels of learning over the course of 5 years.