Color photography has existed since the late 1800s, and there were early color movie film processes basically for as long as movies existed. It’s the quality and cost that eventually got to a point where movies in color became feasible. Color film came later, but you don’t actually need it. Instead you can simply do take the same picture 3 times in B&W with a 3 different color filters (Red, Green, Blue) and then lay them over each other and you’ll get a color image.

At the time, color TV was still pretty early. The NTSC standard for it was out for about a decade prior to the start of the show, and color TVs had been on sale for a while, but they were far more expensive than B&W (think about the price of early HD displays). So, for filming something like the Addams Family, you’d be tripling the filming cost for minimal gain, since you’re trying to recreate the dark B&W look of the Addams Family comics anyways. There were also color TV shows at the time, but again, when most people were fine with B&W at this point, why bother with all the extra work and expense to mimic a desaturated and dark look when you can just do it in B&W?