One thing that the people who argue they've always gone without a phone and can continue doing it the older way is that things are now set up for people with phones. Pay phones are impossible to find, hotels expect you to book ahead (email or website, or phone maybe in some cases), internet cafes are dying, and so forth. Not having a phone or other access to text/data (an ipad on wifi can work ok) puts you at a disadvantage now, when obviously that wouldn't have been the case years ago. Yes, there are trip types where it's less useful but for your average trip it's great.
Many apartments and bnbs, even small hotels, request that you call or text them when you arrive. Can't do that without a phone, and pay phones are mostly extinct. Say your ATM card gets blocked on a fraud alert. All you need to do is call them to unlock it, but without a phone this is a real challenge (remember, no pay phones anymore!). Or say you arrive and your hotel is awful. You're booked for 5 nights but can't deal with this place, it's a disaster. Sit in the cafe next door with your phone, open up a hotel search sight of your preference, find something passable, book it, and head the three blocks over there. No phone? Room finding offices are extinct so you need to physically walk all over town trying to find an available hotel. You may have a guidebook with phone numbers...but how are you going to call them without a phone?
Or say you carefully printed off or hand wrote reams of paper notes and confirmations for your trip. But your bag gets lost/stolen/soaked in a rainstorm. Your paper is now useless. If you had copies on your phone you'd be fine (use the electronic copies, or ask the hotel to print what's critical). As it is, you have nothing. If you're lucky a friend at home can e-mail you some of your info. But how to access your e-mail without a phone? Internet cafes are also going extinct (because...everyone has the internet in their pocket! There are still some, but fewer each year.
Restaurants often require a phone number when making reservations. Some even text you confirmation and will cancel on you if you don't confirm (this is annoying, and not super common, but happens).
So lets say you detour to a nearby town, but you did this last minute so don't have a map. It's Sunday so the tourist office is closed. Buy a paper map, right? Wrong, there's no demand for paper maps of this random town (everyone uses Google maps, and it's not a heavily touristed place anyway).
A simple, silly one - when's the last time you saw an alarm clock in a hotel room? They seem to be disappearing. Sure, you can pack a clock. Or just use your phone.
Sure, you COULD make all this work without a phone. But why when instead you could learn to use a phone as a tool while avoiding the things you don't like. Don't want to post updates to social media? Don't, I agree that can get excessive. Don't want to text people from home? Ignore them, or get a local SIM card and don't give anyone the number. Don't want to browse facebook while in the Louvre? Me neither, it's easy to just turn the phone off. That's the thing - a turned off phone is just a piece of metal, it won't interfere with anything, but once you need it you can turn it on and suddenly it's amazingly useful.