I believe texting and internet on phones are a huge distraction at work. I’m at work now so case in point.
Now certainly, most people are capable of working on a few things at a time, and indeed, many people will get bored, apathetic and complacent if they aren't being challenged, but the opposite extreme is when a person gets a pile of worked dumped on them, and then has no priorities set for them with regards to completion, they will end up being less productive than the person who only has one thing to do at a time.
At my job, we do almost all the work by text messaging. The problem is too many messages at once, and people texting when they should be paying attention in phone meetings.
On the other hand, you can just not reply for a while if you’re concentrating on something else.