Are people now "watching a lot of phone"?
It used to be said of some people that they "watched a lot of television". In those days there was nothing else to watch, in that kind of way.
But how do I describe what is being done today ?
Are people "watching a lot of phone" ? Are they "doing a lot of phone" ? Are they "interacting a lot, on phone" ?
If I say "they are doing a lot of phoning" that would imply they are actually on the telephone, rather than tweeting/facebooking/instagramming/texting.
How else do I describe what they are doing ?
Today in the 21 st century, when someone is on their mobile/smartphone/iPhone/cell phone, that person could be performing any number of different operations. They might be watching a video, looking at a website, checking their emails or texts, sending a photo, or even posting an answer on Stack Exchange. There are so many different functions it would be limiting to say that people are looking at, playing on, videoing, tweeting, or texting, etc. Thus, the simplest thing is to say
People are always on their phones
Google claims to have 259,000 hits for "always on their phones"
People are always using their phones
Compared to the 3,180 hits, which Google claims, for "always using their phones"
P.S. See @laurel's comment below for why Google's estimated results are never truly reliable, and this article which I unearthed.