If your only option is going to be an HDMI 'out' from a cable box, to TVs with no HDMI 'in', you'll likely need to explore adapters that'll take HDMI to component.
https://www.radioshack.com/products/radioshack-hdmi-to-component-converter
"Why" they're doing it is likely cost. Supporting older standards gets more and more expensive (limited suppliers etc) as the vast majority of their customer base moves to 'newer' tech.
HDMI has been implemented in consumer devices since ~2003, I believe.... so 15 years or so of support should likely exceed any warranty period of a TV from the era, so probably what was deemed 'fair and reasonable'.
For the cost of a converter for each TV, you might be able to pick up some newer, used TVs...