The problem is that it often takes a while to look up some information and even small breaks in the conversation leave the other person sitting there twiddling

The problem is that it often takes a while to look up some information and even small breaks in the conversation leave the other person sitting there twiddling their thumbs. Often when someone asks a question, they don't care that much about the answer; they're just making conversation and getting to know you as a person: what you know, care about, and how you react to things. A lot of people are bad at recognizing whether the information they looked up is worth killing the conversation for 20 seconds. Often it isn't! If I wanted to know the answer to a simple question I just asked I could look it up myself. But I didn't! I asked you. That is different from your professor example since he presumably knows so much more about the topic, he can help you learn what to look up. Looking through a photo album together can often spark more conversation and keeps the other person engaged. The same isn't true of a phone.