Using Apple Watch Ultra with cellular plan without having phone on my person

Pulling my hair out talking to support all day. They keep telling me that I need to have my phone connected to the watch in order for the cellular to work properly. The sole benefit of having cellular on the watch is so I can leave my phone at home and stay connected.

Xfinity even falsely advertises this on their website:

The freedom of cellular: With a cellular service plan, you can call and text without your iPhone nearby. Stream your favorite music and podcasts. Get directions with Maps.

Link: Apple Watch - Newest Models & Important Features

Every support agent I talk to tells me that you still need your iPhone with you or else the cellular on the watch will not work as a standalone service. Is this really the case and it's just being falsely advertised? I can't think of a single benefit to the $10/mo line if I need my iPhone on me at all times. This is in inherent benefit of having the phone and watch combo, Xfinity adds no value with the service that can't already be done with a phone line and the watch itself.