I agree it's odd, and I've tried to fix this problem for a long time before giving up...

While we're at it, I wish there was a 30 minutes option! There are many situations where 15 minutes is too short, and 1 hour is too long.

Agreed. Another issue I have is that the requests will randomly stop propagating from the kids' iPads to my phone. To fix it, I have to either reboot the phone or if that doesn't work, change the name of my phone.