I'm a completely naive fan of smart watches (as I don't own one and probably won't any time soon) just because of the possibility to reduce much of what the smart phone provides down to a less attention stealing device. Maybe the notifications are the major problem (I'm naive on this) but I figure that that big screen with an internet behind it is just cognitive cancer. Take the screen away and you're left with music phone calls and an awkward text messaging interface.
Don't know if cellular/network connectivity and battery life can hold up to be practical, but if a device were somewhat larger just to accomodate this I'd think about (less naively).
For me notifications are the main problem, and that's exactly why smartwatches have helped reduce my phone time.
I still carry my phone on me when I have my smartwatch, but even then, it has reduced my phone use. One of the common ways I'd get sucked into my phone was that I'd get a notification, pull out my phone to look at it, and then get distracted by something else. With my smartwatch, I see the notification on the tiny screen, and only take my phone out if it's something that requires a reply/action right away.
Turning off notifications (either for everything or per app) doesn't work for me, because I do want to receive notifications for time sensitive things (ex. "Let's meet at XYZ in 30 mins"), and the classification for immediate action or not isn't based on the app or the sender (one Facebook message might be require immediate action, while another, even from the same person, may not).
It's not perfect; there's still the problem of taking out my phone not due to a notification, but it has solved one major class of problems.
I have - I can happily go without it most of the time. The watch has cellular, and notifications cover most of what I need.
Responding to things can wait till I'm back at a computer. If it's urgent, the watch can make calls, and if you're using a bluetooth headset, it's indistinguishable from a phone.
I don't travel without the phone, though, it is great having easy, fast access to everything (maps, browser, tickets, etc). The watch can do most of that but it's clunkier, and for me it's not a hill worth dying on.
So I do think you can achieve what you're looking for - rely less on your smartphone while still being 24/7 reachable. It is definitely worth looking into.
Don't know if cellular/network connectivity and battery life can hold up to be practical, but if a device were somewhat larger just to accomodate this I'd think about (less naively).