You can indeed do both. That's what separates a good teacher from a great teacher.

But I think we also all now understand that public teaching is one of the worst ROI careers financially and how the few carrpts on the stick (tenure, fairly strong job security) have been stripped away over the decades. The way schools are funded literally rely on real estste value in that area. It's all made so maybe some rich areas get great teachers, but the hopes of using education to crawl out of poverty gets harder and harder. Unsurprising that great teachers leave before their prime or never come in to begin with.

And nope. They do not teach you that in 12th grade econ/government class.