Required? No, that is an exaggeration. Over the past 2 years or so, I've bought about 10 different 43 inch panels from TCL, Visio, Hisense, Sony, and Samsung. All let me watch an HDMI input without connecting to the Internet.
Show me a model number where you cannot plug in HDMI and watch from an input without connecting to the Internet. If this is truly happening, it should be easy to find YouTube and TikTok videos from customers and reviewers.
They include it in the setup screens, but they let you plug in HDMI and it works without internet. Even Amazon Fire TVs (the worst in terms of privacy) has a store mode that removes most of the "smart" features.
Have in mind that newer HDMI cables also allow Ethernet through them. Make sure to get no more than 1.4 (or 1.3, can't remember now) if you want your HDMI-connected device to never request (and get) internet from the host (which is often a PC).
That would require support on both HDMI ports (it's a negotiated protocol, not something that can just be passively wired), and I've never heard of any mass-market hardware that actually supports Ethernet over HDMI, despite actively searching for it on multiple occasions. Discrete graphics cards on PC don't even support CEC, which would actually be useful for some people.
The HDMI standard has it (and the cable generation shouldn't matter, as long as it has all pins connected), but does anything actually implement that Ethernet channel?
The pair used by Ethernet was optional until it was repurposed for eARC (high-bandwidth audio backhaul to a receiver/soundbar). Early-version HDMI cables were available in both "with Ethernet" and "without Ethernet" flavors.
Don't connect it to the internet.