The main example is probably just calling up your parents, whether as a kid or even as an adult calling up their elderly parents. Sometimes you just want to speak to "your parents." You didn't have to decide whether to call mom's cellphone or dad's cellphone. And you didn't have to worry about who you called last. Heck, with caller ID, mom or dad could even decide who wanted to chat with you.
My mother-in-law actually complains about this going the other way. Sometimes she just wants to call our house, because she'd love it if I randomly picked up and she could chat with me in passing. She'd find it awkward to call my phone, because we don't quite have that "chat about nothing on the phone" relationship, but it used to be that you could get two minutes of catching up with someone before you said "ok, now pass me to the person I was really calling for."