The latest piece of Zenith equipment I own is a 1981 integrated stereo (IS 4031), an AM/FM cassette with a BSR changer. Probably the last gasp of the big wide combo units. It states on the back "Mfd. in Korea to the standards and specifications of the Zenith Radio Corp., Chicago, USA." Can't see anything on the inside with a mention of Zenith - did see a resistor lying loose in the back corner though! I'd imagine that, "specifications of Zenith aside," it was a badge-engineered stereo - I've seen Soundesign units from that era that have similar control setups and faceplates.
We had a Zenith System 3 19" color set from the late 80's through around '94 - no remote, had ten number buttons across the top with a green digital tuning indicator - can't remember for sure if it was cable ready (my gut tells me no.) Mom discarded it after the power switch, which was a pushbutton mechanical switch, blew up and shot fire at her one evening