The common factor in all these time-sinks is not the phone, but it's the internet. I have a smartphone and although I could definitely live without it, the only thing I've done is disable data. Rather, I'm too cheap to pay for data. What difference does that make, you ask?
One, on messaging, people would use text to contact me or each other if they notice that WhatsApp/Talk message hasn't reached for a couple of minutes. And a call is very helpful to transmit high density info in short time.
Two, I can still use my very nice phone with a large screen to watch videos, read ebooks on the go like if I'm in a bus or something. The difference here is that these things are not infinity-sinks in my experience - I can go 1 hour or so reading a book on a cellphone but then need to take a break which is when you look up and around. Also, subconsciously, the permanence of the book/video prioritizes real world interrupts (in an embedded programming context) rather than blocking them.
Then, you always have music that you can copy to the phone and listen to if you don't want to put your face to the screen. This enables you to move your head around everywhere and still not be all that bored because you still have that music going on.
If I absolutely want, which is almost never, I play games but I find that mobile games are not something that I like so it never comes up at all.
But a lot of time, I've just noticed myself looking around, just absorbing the world around me and being in my own thoughts rather than a forced stimulus and I find that relaxing unless I'm stuck in a very noisy environment in which case the earphone doubles up as a noise blocker.
And the general trend I've heard here is that you need to be on email. But work already has wifi and if you're at work your computer is right in front of you. Secondly, aren't you making a big mistake by configuring work email on your phone?
Maybe I'm the second coming of RMS but I do not install Facebook and Twitter apps on my phone for privacy reasons. Checking at most once everyday seems to be enough for me but I know that's not the case with everyone. It seems a lot of plans are made over fb for you guys, which is understandable - we use hangouts and whatsapp over here, but primarily whatsapp. But more importantly, for immediate plans we generally use SMS and phone calls which might be why we're not as reliant on facebook. FB is considered more of a public 'show-off' billboard than a private friend group.
So yeah, maybe this was worthy of its own blog-post but my gist here is that turning off the data does wonders. You still get to retain those handy unit converters, two factor authenticators, password wallets and other things that are yours without the Skinner box annoyances of the infinity-sinks.
Of course, before someone rants "You don't know how important it is to have internet on my phone", I'd say you're obviously right. However, maybe after reading my post, you realize that it isn't all that important then kudos to you. You should atleast try it once before knocking it right? A lot of times we think "It's impossible to get through without X" but humans are surprisingly adaptive and can cope without X just fine.
I'm just sharing my experience, hoping that it's useful to you.