I don't have a GP. If I'm ill, I just go to a walk-in clinic. I can also schedule appointments online. When I was too sick to go out at all and due to a particular situation I didn't have web access either, I asked a neighbour to make a phone call for me. I live in a city where I can rely on the help of others.
For some official business, I use the landline at work to talk to banks or government. Most of the time I can use the web, though.
It is not a requirement for me to have a personal phone.
Regarding the GP, this is presumably dependent on the country you live in. In the UK you have a specific clinic you sign up with. None of the 4 clinics I've used have taken walk in appointments, all have required phoning that morning to get a scheduled appointment that day.
But whenever we went somewhere they suddenly needed a ride.
Getting in touch with a GP? I can use the internet. Bank fraud? Same, or just go to a branch.
As far as accidents and emergencies are concerned, these are no different than the solutions pre-smart phone or when your phone has broken, out of power, or if you forgot it elsewhere. You go to the nearest house. Landlines wouldn't call 911 for you if you dind't have phone service. Besides, folks can keep a cheap non-smartphone with no service in their house which allows you to call 911 in an emergency. Everything else can be worked around.
All it would really take is a knock on the neighbor's door and ask them to call the cops for you. The vast majority of folks won't turn you down. If all else fails, go to the nearest gas station or fast food establishment. Chances are they'll happily call for you.
Lucky you. My GPs website has phone number and an address on it. My bank are equally as unhelpful. They have internet banking, but there is no way to suspend a card or re order a new one without phoning them. Last time I had an issue with my card I was out of the country so visiting the branch was out of the question (not to mention the branch is almost 2 miles from my home, has no parking and is only open 9:30 to 5 Monday to Friday, when I'm working). There's no technical reason they can't do this online, they just don't currently.
As much as I'd like to not have an active phone, it's not really feasible to live todays world without one. You're relying on other people to have phones so that you don't have to carry one. Your suggestion to keep a cheap non smartphone defeats the purpose of not having a phone.
But I was alive before the smartphones were available and didn't always have money for phone service and rent. So were a lot of folks I knew. And i simply understand the ways folks can get around having phone service... even if I think it is personally weird to do so out of choice instead of necessity.
I have also been in situations where I don't have the phone for a variety of reasons: Not working, for got it, spotty service, and so on. Of course you have to rely on others in these situations, the same as before everyone had such things. Actually being in an emergency has been a pretty rare thing, with or without cell phones. I've called 911 a few times, but only twice when not at work. Once for a car accident outside the house (a pretty bad one, lifeline helicopter and all), and one for someone's suicide attempt.
As a side note, it is a shame that the doctors offices do not have it. Most of them have it around here that I have seen. I avoid calling unless absolutely have to. As a bonus, the phones here are such that if I've run out of money on my prepaid phone, folks can still call me.