Even in things like "The Jetsons", the TVs were giant CRT units. I guess nobody back then (1960's) had any inkling of the flat panel monitors to come.
Actually,there were several flat panel technologies mooted during the 1950s & '60s.
Some of the concepts were a bit extreme,like the thin CRT where the beam made two 90 degree bends,prior to scanning (I'm not sure how) the screen.
Another one in the '60s had thousands of tiny cold cathode electron guns mounted extremely close to a phosphor coated screen.
They were meant to be turned on & off digitally,but their beam intensity would be controlled by the analog signal.
The very first experimental plasma screens were made in the late 1960s,too.
What nobody predicted was the change from 3:4 to 16:9 aspect ratio.
Remember,the people drawing "The Jetsons" were not technical folk,they were cartoonists!
One thing I found delightful in one supposedly "more realistic" cartoon series was where a "NASA -style" control room was shown,complete with lovingly animated vertical blanking bars drifting up the monitor screens.
This of course happens with real movie film,or TV shots of these places due to the fact that the blanking is not in sync between the display & the camera.