No disagreement with your argument about being protective about one’s time. But in your case you haven’t negotiated anything. You just go when you have to.
This all comes back to the fact that everyone should be protective of their time. I’m single but regularly run errands, exercise, go grocery shopping etc in the “middle of the workday”. I get my work done. Nobody complains.
It’s just a matter of knowing and recognizing your own value.
Parents needing such negotiations may be a "hidden cost" that y'all aren't considering. Also, parenting is a ton of work so when I kick off the paid job, I'm still working 'til 9 most nights.
Out of curiosity, was there ever any situation that your manager would reach out and ask for you to put additional time because of an urgent requirement / situation?