The school should have fired your mom. Students don't always have free time that aligns with instructor office hours, and some issues are best addressed in writing. Whether they like it or not, communicating with students through a variety of channels is absolutely part of a teacher's job. Those who don't want to do it should find another line of work.
This is a misunderstanding of the job of a professor. (I have some experience here.)
Our job is to teach well enough, to research well enough, and to handle administrative stuff well enough, in a context where any one of those could easily be a full time job and it's impossible to do all of them perfectly.
Having a work pattern in which the less important stuff falls through the cracks while making sure the important stuff gets handled is necessary and common. As long as people understand your pattern and can work within it it's generally ok.
Do you expect your mechanic to open their shop at 10pm to work on your car around your schedule?
One of my favorite professors put it in a different way. The classic approach is that they are lecturers first, and not teachers.
The professor is the master in their field. They go into class. They lecture on things based on their experience, answer questions, then leave. Students are there to make use of the faculty and the department to achieve their goals. If someone wanted to invent YouTube, they would go to university to study under someone who had invented some complex video compression & streaming algorithm etc. This is where universities output the outstanding individuals.
But in the 21st century, many universities are simply teaching institutions. They make sure the student understands and guide the poor ones. They make mediocre engineers, but dams and highways are built and maintained by mediocre engineers. The government unis were funded per head; literally the goal is to fill the lecture hall with as many heads as possible.
So I don't entirely disagree. In the end, my mom was not promoted to the level everyone expected of her, probably due to things like this. I do believe she actually replied to the important or thoughtful emails and just built this image of inaccessibility to seem fair to everyone.