Rote learning is out, we know. We know, because it stopped being useful, and curriculae are now being changed to account for that fact. We are responding to a technological reality that requires high levels of expertise and logical thinking. Just knowing how the world is, isn't good enough; now we must know how to make it.
There is a second, slightly more invisible demand, though, and that is that the kind of motivation one need for doing such tasks is wholly different for classical work. Doing highly technical work, keeps you very many steps from those who benefit from your work.
Perhaps you are working as a programmer on communications system. You might then only your part on an aspect of a system, designed to better productivity in another job, that isn't even then directly tied to people's everyday needs. Such work situations increase the demands for inner motivation. and the skills necessary to understand your place in society. And that basically means, learning philosophy.
Philosophy, ever since Socrates, became a discipline for learning how of live well, and remained so roughly until the enlightenment. And, while the tradition has been with us, it has been toned down in favour of hard nosed academic philosophy. But it is this living well tradition that will be crucial to a modern worker. The aim of such philosophy is to learn how to be an autonomous and good person; which is learned through a tripartite program; learning logic, ethics, and physics. Or, how to think, how to live, what is real.
The clearest expression of this tripartite route is found with the Stoics. Ethics was the goal, they argued, but to get to it, one needed a command of logic. The idea of logic in the time of the stoics was wider than our current conception. It included learning how to think, how to write well, argue and analyse. Logic was the tool that was to open up a wide analysis of lifes problems, and grant you access to the higher faculties of reasoning. Analysis, though, will not help you if you don't have the proper material to do an analysis of. Here, one needed to know something about the composition of the world, which would provide the raw material for your query. Together these become a philosophy in the strict sense, a search for wisdom that is a life project, and not a motivational poster.
There are always dangers in engaging in such grand projects such as "learning philosophy in school". How does one insure that we just supplant one dogma with another? Hopefully this is countered by a demand for critical thinking, and if it isn't - well, we tried. The main goal ought to be that, whatever work one will be doing in the future; one will be able to make rational choices, and the choices here is the important part. Moral actions come from personal initiative; which is not only a moral truth, but also a sociological one. Groups tend to do worse in difficult moral situation, due to an effect known as a diffusion of responsibility, where everyone feels that others could do something. Such effects can only be countered by a rational readied mind, or as I'd like to think of such people; as autonomous individuals.
Besides the work place benefits, there are learning benefits as well. Standard pedagogical knowledge today teaches that bridging knowledge between subjects, and understanding the intentions of the writers of technical material is crucial for good learning. Philosophy can help make these bridges by taking an overall outlook of knowledge and learning.
Start them in first class, philosophy as it's own subject, and drop the greek. Teach them how to effectively think, how to think about acting, and how to connect the knowledge from all other subjects, that is "physics".
Regarding classes such as religion and social science, we could learn in a philosophy what good a religion can bring to our lives, or what social science can teach us about humility. For mathematics, we could take a deeper look at what counting actually is, and what uses the = sign could have for making analogies. For english, one could look at how words change us, and how we change words. In the end, philosophy can be used as a key that opens up life for us in a new way, and gives direction to our activity.
Philosophy has the potential to make us better learners, and better people. I don't need any other reasons than that.