I travel with both AT&T (through a Mobley) and Verizon (using a Jetpack), both with unlimited data service (which, of course, is not really unlimited). Between the two, I have had data service in most parts of the country, but there are exceptions. A few off the top of my head are Big Bend National Park, Sunny Flat Campground, Coronado National Forest in AZ, & Cades Cove in the Great Smoky National Park, all with no internet or cell coverage.
You are always going to find places that don't have internet service, but they are getting fewer all the time. I think you will find satellite service fast enough to stream video more difficult & expensive than practical, at least until Musk's Space X service arrives (if ever).