I'd disagree. Some anecdotal evidence - I'm from a HCOL suburban area with a nationally ranked public school system. Teachers here are generally considered "well-paid" by teacher salary standards. Many of the teachers in my area literally cannot afford to live here, and have to commute 30-40 minutes in.
My mom was a teacher there. She was making about $80k a year at the end of her career, with 2 masters degree and 20 years of experience teaching (so she was pretty much maxed out on her salary). Her pension is something like $20k a year (also maxed out due to her YOE). My dad was in between jobs for some time in there, and my parents, who are frugal people, struggled to make ends meet on just my moms salary, borrowing against their mortgage for the year while my dad was unemployed.