~dogs eat literal shit (especially puppies, oml). a lot of the time dogs will lick their owners body to show their joy. you can put those two together, right?
~dogs need to be taken for a walk in order to be able to poop. dogs are the pinnacle of uselessness and inability, cats on the other hand don't put themselves beyond their human companions. or, as kanye put it:
'you see there's leaders / and there's followers / but I'd rather be a dick / than a swallower'
~when dogs poop in public you are forced to pick it up
~dogs need training, all cats need to know is where the pooper is at
~cats kill mice, rats or whatever pest is prevalent in your region, dogs chose rabbits or foxes
that is all
Dogs that're parents may hide the smell of their infant's poop so predators don't find the scent. It's an instinctual thing that served them well in the wild back when they were wolves. Most dogs don't randomly eat shit for no reason, I've had 3 dogs and taken care of a few friends/relatives dogs and I've never seen one of them eat shit so far.
Dogs can learn to use a litter box or poop in any specific place you want, they do not need to be taken for walks to do it.
Dogs are clearly not useless, they're useful for many more things than cats are. Guide dogs, guard dogs, herding dogs, bomb/drug/anything scent dogs, hunting dogs, rescue dogs, etc. etc. Cats just kill rodents and birds.
Dogs do not choose rabbits or foxes. Some dogs even buddy up with foxes. Depends on the type of dog. Many of the terrier breeds, including the rat terrier, are excellent at killing vermin.
As for dependence/independence, and submission/dominance it depends on the breed. Not all dogs are inherently obedient for nothing or submissive, you have to communicate with them well and give them what they want. There are even dog breeds that can/do still live in the wild if they have to, and obviously some wild dogs still exist.
My current dog, all we had to teach him really was to not try to herd us too much, and basic potty training. Was done within a month. After that he's been extremely easy to have around. It doesn't take that much to get a dog to cat-levels of good behavior. The only thing is that they will usually desire more attention and interaction with their owners than a cat. If you're not into that and want a pet that's more comfortable being ignored, that's why you'd get a cat. Or you could get two dogs to keep eachother company although that can be tricky.
Most dogs will do better without the submissive/dominant relationship, certain dogs prefer that or even want to be dominant. But, in the wild, wolves usually grouped up with their own family not a rigid hierarchy with an alpha male or whatever. The parents were the leaders but not in a domineering way. It's only when packs of unrelated wolves form that an alpha leader has to be established.
However dogs clearly aren't wolves anymore either - a few breeds are more wolf-like but even those are far from a wolf temperament wise, and almost all breeds(excluding those bred for dog fighting and such perhaps) are more cooperative and friendly by nature than wolves so even unrelated dogs can potentially get along without any power struggles.
Dogs are more social than cats, so that might make cats seem more self reliant. But that doesn't make them better partners with humans or better animals. In fact most social animals have higher intelligence than solitary animals in general.