While it's probably true that SF has more homeless due to migration, I don't think it's the root cause. You really have to look at the societal structure, government support and so on for the causes.
I don't think this is terrible, but it has costs associated with it that will become apparent further down the road -- similar to how the existing education system born from the industrial revolution's needs has proven to. The system you have suggested has a prominent lack of means to introduce people to advanced theoretical physics, economics research, astronomy, abstract mathematics, etc, you get the picture. A generation without a hint of knowledge in the non-practical fields will function fine in the short-term, but it will lead to a stagnation of advancement until an external trigger brings it back about.
Essentially, as I'm guessing you're a hacker-hustler-type, you see the primary course of education to promote passion in "doing," and that's my first instinctual priority for education as well. But classically, education has had a role to do much more than just that (albeit extremely inefficiently) for many generations, and it could be detrimental to focus on only one educational priority of "learn to do things well", with a potential to lose being able to gain exposure to other kinds of intellectual commitments. Maybe it won't happen, but it's a real risk. Who knows what we may have lost already from generations past?
Of course, everyone in the world agrees that the "sitting behind desks competing on test scores forgetting all the knowledge and then stumbling through relearning the real world from scratch" model of today's education is broken and pretty stupid, but it's not that straightforward to fix, unfortunately. Your suggestion is definitely something a single school could adopt (and broad institutionalized educational requirements should be abolished), and I would love to send my future kids there over anything that exists today.
I do think the northern European schooling/education model makes a lot more sense, and could be a solution for a lot of the societal problems at the root. However, the cultural diversity of SF makes that a much more complex problem than it is in Sweden/Finland. And so we come full circle, this stuff is just not that easy as "look it works over there, we should do it too"