That's where you're missing the point. Smart watches have become popular because of the fitness component, and have also shown great versatility beyond that, including invoking a voice assistant and screening notifications.
I haven't taken my phone off silent in years, I will only have my watch on vibrate and a select few apps filtered to send notifications to my phone. The rest are not of immediate consequence, so I don't get them "in real time". Plus, if the watch is off my wrist, it vibrates my desk just like a phone. Notifications are dismissed automatically after a timeout, or a button to dismiss.
I find my glasses come off for far more serious activities than my watch. I never intended for my watch to be a phone replacement where I can respond to messages, but it's sure good at letting me know a message needs my attention.
A few things a watch offers you while lifting, specifically:
- rep counting
- heart rate monitoring
- music, without a phone, by pairing a BT headset directly to the watch
A few more things smart watches are great at:
- forget your wallet in the car? Contactless payments. Or, buy a bottle of water in the middle of a run or bike.
- sleep tracking
- leave your phone in your pocket more and enjoy life
- don't even bring your phone on a run, built in GPS tracks for you
- don't even bring your phone on a bike, same reason
- built in topo maps for hiking
When you think about it, smart watches are /far/ more useful than they seem because of all the tech and sensors packed into a device that (potentially) lasts days at a time. And I think most people get that, which is why smart watches are already a huge industry.