The Apple Watch is unquestionably a better smartphone than the original iPhone. Granted, the original iPhone isn’t a very impressive smartphone by today’s standards — but it was mind-blowingly revolutionary and extremely useful back then; it’s just that today’s smartphones do all that and so much more as well.
The biggest caveat is that there are things you might use the Watch for where all the “heavy lifting” is done by your phone.
The most significant of those is generally SMS. The Watch is incapable of speaking SMS, so it uses the iPhone as a relay. However, the only requirement here is that the Watch and iPhone have to be able to communicate in real time, and that the iPhone has to be able to talk to the SMS network. So you can leave your iPhone powered on at home, connected to WiFi, and use your Watch on cellular when you’re out and about and it’ll transparently “just work,” with all the obvious caveats about how something that complicated can be brittle. (Note that Messages is handled by Apple’s servers, so this only applies to SMS.
There are, however, other applications which require that the Watch and iPhone talk directly to each other either on Bluetooth or the same WiFi network. The 2FA app the university used was the most annoying of these when I put my iPhone Xs through the wash a couple years ago, but I was still able to get a phone call on the Watch and complete the authentication. The app that controls my hearing aids is the same, but I personally almost never need to use that app.
My current iPhone is a 13 mini, which I don’t mind carrying with me whenever I’m out and about. But my next iPhone will be a current-model Pro, possibly even a Max — at which point the iPhone becomes a small tablet that gets left behind whenever I think I can do without it.
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