For me that actually is a symptom of having some sort of problem. He actually somewhat admits that.
If someone says: "I hadn't had a drink for months and I feel great, I will never drink again." Good for you, honestly, but you know the opposite of total abstinence does not have to be to get drunk until you blackout two times a week. What's wrong with having one beer at a party, a glass of wine to dinner? If you have to drink 10 beers because you can't control yourself, then it seems like you have a problem, though whatever works for you. If the only solution is abstinence, then by all means, do it.
He has a problem in finding a reasonable balance. I am also glad he readily admits that a phone is a symbol of his own stressful life he once had, so he rejects it for that reason mostly.
Now I won't deny that I am in a somewhat different position, since my schedule is not nearly as busy as his, and the metaphor does only work to a certain extent, but I for one tend to not use my mobile phone that often. People know they can reach me if something happens, at least in theory, since they know I don't check it that often.
It's on mute most of the time, and if I don't want to take a call, guess what, I don't. And I mostly communicate with E-Mail too, but I can do that from my phone.
I call people back when I have the time, I also always have it with me, I can enjoy the comfort of any application I want to, but it certainly does not control my life. And with a modern phone you actually can streamline your experience a lot (give your contacts various priorities, some can reach you, some can only during a given time frame and lots of other things you can do). I guess on an old Nokia, you can't do a lot in that area.
You don't need to take a phone call when you don't want to. You will have to deal with people saying "Did you not have your phone with you?" and if the answer is "Well actually, I did" they might get a little bit angry at first, but being available is not something you have to be at all times. People in my circle all know how I stand on this, and I read Telegram Messages and sometimes reply days later, if it's not crucially important. They are used to it, and it's not an issue these days.
So while I sympathize, it's not "being enslaved" versus "being free", there is a healthy middle ground we should aim for. It takes work, adjustment, is not maybe as easy as just throwing your phone away, but it's worth it.
PS: I don't like touch either, my mobile phone has a physical keyboard and I am happy with it.