Also we keep thinking the important thing is that they're computers but actually the important thing is the Network. So in a way phones (which are all about being connected to the network) might be the best term anyway even though we rarely use them to make a voice call.
When I was in Korea, the term "handset" seemed ubiquitous among the English-speaking people I interacted with. This is even stranger because, as I understand it, the Korean term is a transliteration of the English "smartphone", so I don't know where people were getting "handset" from.