I think this is a generational thing. Older folks don't see phone calls as intrusive. We've grown up knowing that it is OK not to answer and just check the messages later. And the days of screening calls by letting the machine pick up.

So this: "By calling, I'm implicitly demanding his/her time right now." is just a projection of your own opinions of phones onto someone else. Likewise not knowing who to speak to - you call, let someone answer, tell them what is up, and let them point you to the correct person. No biggie. It is how communication worked in days of yore.

I'm not saying you need to change your attitude about phones - hate them all you like. But not everyone agrees with you, so if you sincerely are wondering why phones still exist, it is because different people exist.