Yes, and it is not unusual for a teacher in the CPS to make over $100 K per year
I attended school there, in particular a very highly rated and selective admission one called Lane Tech. All of the teachers had worked in the field they taught, it was also a vocational school
More recently they scotched the shop classes and went into some computer stuff but it is still the best HS in the CPS system
So to your comment, I know a lot about both the model as well as the student population. Where I went we drew from across the city and our population covered every demographic.
CPS is a mess and they know it and do not care, just pay the Union Members and there is no passion for excellence anymore
The relationship is not vague as you posit, it is tangible
My point is that level of funding is not determinative of the level of education the students at a school receive. It is not wholly irrelevant, but it is at least the 4th or 5th item on the list - as is suggested by several points in your response.