IMHO it is not the Internet that's the problem. The constant connectivity is killing productivity.
Every morning I used to start my day with reading HN, on the bus to school I surfed the web. At uni, on every break I used to take out my phone and browse some more. After school I binge-watched TV shows and surfed more. My attention span got so divided that I couldn't concentrate watching a single episode, I constantly switched to a browser to surf more.
I learned a lot about programming, but my personal life suffered.
I couldn't meet deadlines, couldn't study for uni (studying law).
In the end I concluded that I had developed something like an internet addiction.
Furthermore, it wasn't just limited to internet. I stopped changing clothes, stopped keeping my already cluttered room in a somewhat liveable standard, stopped caring for my health, ate a lot of junk food, got hooked to TV-Shows.
Now, instead of constant short bursts of divided internet surfing, I am trying to set out a time for surfing. And outside those hours, I go offline.
It has been a though switch, but I slowly feel that I'm getting my impulse control back.
I recently started reading Deep Work by Cal Newport, I can recommend it to anyone trying to get off the vicious cycle.