It's a little strange to see people scramble to replace their phone with other things. Before smart phones, or mobile phones in general, I'd carry my wallet and keys, nothing else. We can still just do that, it's fine. If you replace your phone with all this stuff anyway, I don't really see the point. Sure, bring a book if you're traveling, but we don't need to listen to music or be able to watch a movie all the time. It's okay to be bored or just observe your surroundings.
The social pressure I don't get, I think that's a made up excuse. I'm never encountered anyone say anything beyond "Oh, okay" if it comes up that I left my phone at home.
Not social pressure as in "your phone sucks" or "you have green bubbles". That's stuff for kids and "grow up" is indeed the correct response.
But many social groups use stuff like whatsapp, and it's more or less expected for you to be reachable. It would be healthier if we didn't to that, for sure, but often you don't feel like burning your social capital on "guys, hear me out, let's use some weird-ass tech for nerds you probably don't care about at all".
I think it's driven from an understanding that being constantly connected is potentially unhealthy for ones mental health. Not saying that's 100% true but I think enough people feel it that they are looking for solutions in things like dumb phones, digital detox, purpose-built devices etc.
I understand your lament about people just being able to be bored, but I think this gets at something deeper, that when we aren't bored and do want to do something, we are often distracted because of the nature of smart phones.