Someone isn't a "bad parent" for not teaching their child their number, but yes, there are times when it would be very good for them to know. We have had this happen several times in the ER. The person is not seriously injured, is awake and alert, but can't call any family because their phone was damaged in the wreck and they don't know the numbers.
The saddest was a 14 year old boy who had broken bones, and had no clue how to reach his mom. No clue. He knew his name and address, and his parents' names, but not their cell phone numbers. They didn't have a home phone, only cell phones, so we couldn't look it up. It never entered our minds to think that his mom was a bad parent, but rather, that he just didn't see the need to learn the numbers (since they were in his phone) and so he hadn't bothered.
So if your kid doesn't know how to reach you, expect it to take longer to get notified if something happens to them.