Broadcasting uses a highly limited resource, local TV freqiencies. Especially until recently, these were really limited to a dozen or so channels per metro area.
There are far more than a dozen websites out there.
Many people historically only had a single phone provider available at their home. Last mile internet isn't competitive for most people, I would agree they should be considered a common carrier. This concept of "common carrier" is important in this debate.
A train line that is the sole means of commerce in and out of a town is a common carrier. There's no competitors really possible to enter into that market. For that train line to decide to not run certain cargo outside of safety concerns is to then control all the commerce with no reasonable competitor.
Literally right now I'm watching streaming video content hosted from some service other than YouTube. I probably spend less than an hour a week watching YouTube content. It's hardly the only rail line in town, nor is it the only way I can view video content. Now if the only viable ISP said "you can't connect to YouTube, if you don't like it sell your house and move to the next town over" then yeah that's a common carrier and shouldn't be allowed to do that.
DNS names aren't limited by the US government. There are lots of TLDs which are controlled by other governments. And largely they're pretty much managed by lots of different corporations. Either way, the government directly getting involved in taking over your domain name without any due process just to silence your speech probably does become a first amendment issue at least for US nationals. Either way, they're massively less limited than how many effective TV freqiencies or phone providers are in a given metro area.
There are far more than a dozen websites out there.