You know, when you put it that way, that does raise a lot of good points. There are legitimate non-obvious problems in this area ("family resource management" might be a catchy name here) and not a lot of solutions. And the solutions that exist are so heavyweight and industry-tailored that when you hear about parents using JIRA, it just sounds absurd (and rightly so).
Probably the reason there aren't many such solutions is that it's not a sexy or obviously lucrative field, and that it's probably pretty hard to come up with a well-designed product that handles all the complexity of a family. I mean, come to think of it, most software startup founders are young and have few commitments (e.g. children); I can't imagine them being able to empathize well enough until they're at a later stage of their lives. But, perhaps someone's working on this as a very extensive side project.