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Yeah, it depends on your individual circumstances.
I go out running to get away from things (including my phone). I don't ever plan a run where I'll need money and, right now during the pandemic, the furthest I ever get away from home is about 2 miles (even on a 10k). My runs start/finish at home so there's no need to carry anything more.
My "next level up" is the small rucksack, which is quite a big jump in terms of being able to carry more stuff.
Nothing -> Armband -> Flipbelt -> Small running rucksack or running bumbag type thing -> bigger and bigger rucksacks...
The main reason I suddenly thought I needed a phone today was that I really wanted a coffee after my run and was worried I didn't have enough money on my card - if I'd had my phone I could have used that!
Likewise if I'd needed to get on public transport if I'd got a puncture etc.
I don't listen to music but my watch is pretty much the most basic available (Forerunner 25) so a phone would be good for that too.