Like a lot of academic jobs they are deathly afraid to allow any job to go part-time because then they fear they might lose funding for it as a full-time job, or lose funding for other full-time jobs in the same department, in the future.

They also don't want to do job sharing because it makes the benefits picture dicey. They don't want to pay health insurance benefits for two part-timers.

It's a mess. Tying insurance to work screwed everyone.

To some extent it could be flexible. I worked a lot of nights and weekends as an academic librarian. But the forty hours was just too difficult with kids. The pay is also terrible, so you start to wonder why you are paying more hourly for childcare than you can make at your job that required a master's degree.