Actually, bedbugs DO eat each other. Of course, bedbugs don't have teeth - or mandibles - so what they actually do is suck the guts out just the same as sucking the blood out of mammals, or the same as a spider eating any insect or bug, and, as with a spider, there is an exoskeleton left behind. The difference is that after a little bedbug has been eaten by a big bedbug, the body left behind is intact but hollow. A spider would have wrapped it in silk and a harvestman (like a daddy-longlegs) would have crushed it. And when they are shut in a room with zero (0) other sources of food they do, in fact, turn cannibal. It's one of the reasons they are so hard to get rid of, because you think the food supply has been cut off and the young'uns have been poisoned, but the young'uns have been eaten and the old'uns are still laying eggs.
As for cats not being bothered - the bedbugs you had may have been humanocentric, but the ones I had weren't. My cat had bites on his stomach, where the fur is thin. Not nearly as many (even per square foot) as my son, who, as a teenager, not only slept like the dead but was not subject to a full body inspection by his mommy. It was his room in the basement that got so heavily infested.
Oh, and before you point out that creatures with exoskeletons shed them as they grow, let me point out that creatures with exoskeletons shed them in _sections_ as they grow. They can't crawl out of the old skeleton if there isn't a hole in it. With the few bugs that do this type of growing, the head usually falls off and then the rest of the body is shaken off, or else the carapace splits down the middle, leaving a single piece split open like a stuffed baked potato with the stuffing having walked away. While I didn't examine the remains on the floor (just the ones on the wall to determine that they were remains), given the black, gritty residue that bedbugs leave behind them, I suspect that they shed their exoskeleton in chunks. Certainly there was nothing like the whole carapaces covering my son's wall in the remains on the edges of my box spring. _I_ was changing my sheets regularly and actually turning on the light when I went to bed & got up. It is very fortunate that my son has a severe fear of flying because I don't even want to think about what would happen to him in a tropical climate.
On the upside, he does change his sheets at least once a month now.