Here in the Netherlands, already a generally densely populated country, there's a teacher shortage everywhere, including cities.

People rather have higher paying jobs, or quit because the job disappoints. I belong to the latter group. I quit teaching at secondary school (ages 15-18). After three different schools in three different areas, and having spoken with many colleagues and their experiences, I sadly had to conclude that broadly the work culture in secondary education (in this country, at least) is dramatically lacking professionalism. To a point where I think if my goal is to teach the next generation well enough, my time and energy is better spent elsewhere.

Around here, a lot of new teachers give up after 1 year. After a draining day in the class, checking their homework, prepping the next day, the governement gives teachers an additional mountain of paperwork to fill in, and parents want to discuss everything.

A second problem is kids found out they can get everyone fired for claiming sexual harassment. Especially male teachers are scared. A brat utters a single sentence and you'll never work again as a teacher, and all your neighbours hate you.

Teaching today is a bad job.

> Teacher shortage mostly happens in sparse communities not dense ones since it is easy to find teachers where lots of people live.

Only in medium density cities. Once you get to very high cost of living areas, finding and keeping teachers becomes extremely difficult because there's just not enough money to pay them enough for the cost of living. Many teachers either move to cheaper areas or change careers to high paying jobs.