This is true in the same sense you don't need to own a pair of shoes.

Technically, sure, but there are jobs that require you to have a phone (at many different career points too), colleges that expect it, and more. And while there may be workarounds, they are often workarounds at someone else's expense, such as asking someone else to check the class schedule or work schedule.

So yes. You don't need to own a smart phone. And you don't need to own shoes. Both will get you (understandable) looks from general society. Both will limit what you can do. Both are somewhat understandable as having become a default, expected thing that people WILL have.