Per analogy, one could probably argue that you need a phone of some sort (per professional expectations).
Job hunting: This would be significantly harder without a personal phone, but regular trips to a recruitment agent's office could make it possible. I can certainly see that it would be a significant advantage to have a phone.
At home: Hugely depends on how far and wide your family have spread. If they are all within walking distance, then you don't need a phone. Sure it's more convenient, and sure, you'll spend a lot of time outside people's houses wondering if they're actually in, but that's how I grew up without a mobile phone. Interestingly, I would counter-argue (with myself) that you do need a phone if you are the only family member in a remote area, if only for your mental health.
Emergencies: Yes, sometimes you just need a phone.
So yes. A bit need.