Stations can brand however they damn please so long as they run FCC identification by flashing their callsign and channel number in tiny print for five seconds every hour. The branding is a completely different issue.
As true as that is, it would look completely weird, if they don't at least reference their call sign within their branding on a regular basis outside of the hourly requirement. I say that because it's happened before. When On TV created a subscription service over local channels, the only branding they used outside of the local identification, was On TV, and the local identification looked out of place, compared to everything else they did branding wise.
You need to incorporate the call sign into the branding so that the required local identification doesn't clash with the rest of the branding.
I think it's entirely possible to not use the callsign in any element of the branding. That's what the majority of the network-owned stations do ("CBS4" etc. etc.)
Except that's not quite the case, because they still have to do the legal ID at the top of every hour, so whilst the main part of the branding might not include the call sign, you still have to find a way to incorporate it into the branding for the legal ID.
Of course this is all complicated by the fact there may be one brand used for all non-news output, and the news output might be branded differently. WNBC uses NBC4 for their non-news output, and News 4 New York for their news output. Previously they've used NewsChannel4, which almost feels like a channel branding.
I had to look up what On TV is. Interesting story, though I'm not sure how much bearing a pay network from the 80s has on lessons for TV branding today.
There are lessons to be learned from every era. Just because something was 30 years ago or more, doesn't mean that it has no relevancy or bearing to today. You just have to look at the era it happened in, and adjust accordingly.
In many ways to me, it feels somewhat ironic that today's branding mostly feels weak and unmemorable, compared to the analogue satellite era, or the four channel era, or even going as far back as when BBC and ITV were the only two channels out there, and many of those brandings were very memorable. Come 20 years time, we might be looking back at this time and thinking how bad and weak the branding was. A time when branding was arguably less important than it is now, is often remembered for having better and strionger branding, than today's channels. It seems counter intuitive.