It's actually funny you mentioned the lack of indicating call sign or operating location. I saw something similar done on purpose.

I worked at WCCO in Minneapolis briefly a few years ago. Right around that time, CBS corporate was attempting to standardize all their stations and associated websites. In their mind, that meant making everything "CBS News [Location]" and stripping just about everything else from the public marketing.

WCCO, KPIX in Los Angeles, and a few other stations battled back about this because the local name recognition of the call sign was stronger than CBS would be by itself.

So now, when you bop around the "Local News" section of the CBS Website, some cities have logos with the call letters, and some do not.

In short, when you see a station that that's difficult to identify, try finding out who owns it. Very often the ownership is to blame for one reason or another.