Yes, definitely. Because most of the dogs that would actually be looked after would be great for a variety of other tasks - everything from being service dogs, dogs that check for illegal substances by smell, police dogs, dogs who can herd animals and a variety of other tasks. Even new tasks that people still haven't been able to offload to canines.
If the animals can provide more value to humanity and will be allowed to become smarter and somewhat evolve, i think it's definitely worth it. Otherwise, if selective breeding for utility wasn't a thing already, we probably wouldn't have breeds that are passable for any of the tasks above.
As for wild dogs, this hasn't ever been a major problem in my country. I haven't seen any, there have never been any news stories about people being bitten or killed by wild dogs, i don't know anyone who has had run in with them and frankly there are bigger problems in the country - things like racoons and other small animals that carry rabies, foxes and the occasional wolves that kill off young deers and does alike, beavers that build dams and flood portions of the forest and so on.
Edit: looked for any studies that i could find, sadly there were none that'd attempt to quantify how many stray dogs there are in the country and how many of those have attacked people and how many have attacked other animals. Just found a news report of one person being bitten by them: https://baltics.news/2021/03/16/in-rezekne-region-a-woman-is...
Just to be clear, i am not attempting to say that wild dogs are not a large problem, just that it's not a problem everywhere to the same degree and that quite possibly there are other social factors at play - why would there be more wild dogs on one region of the world as opposed to another, especially when humans are the ones who breed these animals in the first place? Do the people not look after them? Are there puppy mills that get abandoned? Do people generally not view having dogs as a great responsibility? Are there no services that take care of wild and stray animals?
It's not like humans couldn't do anything about it either - if wild dogs are an inevitability in certain parts of the world, why not disallow "importing" dogs of these breeds to those regions and disallow breeding them there?
Here's an example of concentrated effort in regards to eradicating rabies in the country, i don't see why something similar couldn't be done in regards to stray animals (though it may only work on a smaller scale like in this country, at least without lots of coordinated effort): https://ec.europa.eu/food/sites/food/files/animals/docs/reg-...