I only use my watch for text messages using LTE. Very rarely a call when I 'need' to answer it for a few seconds. Like my wife calling instead of texting me - got to be important.
During work, I take a couple walks of about 10 minutes each with just my watch, no phone. I either go swimming/playing in the pool or bike riding with my kids at night in the summer for about an hour. Just my watch, no phone. I also go for walks with just my watch. Pretty much any activity I do outside, I don't take my phone. A lot more freeing.
I also referee football and lacrosse. I can't take the phone on the field with me, so I'm still connected on the field and know if something is an emergency which I wouldn't know until I got to the locker room. It's also great looking at radar for approaching storms.
For example, I had a situation where I was doing a game, and didn't have any communication on me. My wife went into early labor (before 8 months!)... totally not expecting it... I couldn't be contacted. A friend of mine actually drove to the game, got onto the sidelines and stopped the game to let me know. I left the game and I missed the delivery as I was 2 hours late getting to the hospital. If I would have had an Apple Watch LTE at the time, I wouldn't have missed it. So this situation makes me confident to know that if something like a parent in the hospital, someone dying, or something, I will know and be where I need to be.
This is my exact use case. When I go on walks, go to the pool, ect it is great not to have to worry about my phone while still staying connected. I also coach my son's sports teams and I always hated carrying my phone with me during practices and games. Now I can leave my phone behind and stay connected with my watch for texts and emails. I love it.