Primary factor in my opinion:
People like children and family life, most people will want to have a family. the viewpoint that it is/could be morally wrong to have children is very uncommon outside of some western and internet based communities, in fact Im fairly confident the opposite (that having children is morally good) is more common
most people consider their lives worth living, therefore would presumably consider their childrens lives worth living
A few other factors:
in cultures with the highest birthrates, starting a family is often considered the default, and it would be a specific and unusual choice to not do that
Education for women, wealth, and access to birth control are all negatively correlated with birth rates
You mentioned some of these, but I think the strongest take-away here is that you are assuming most people share your viewpoint on several very specific and not-universal moral codes which suggest that people should not only not have children under certain conditions (eg poverty) but also go to great lengths to avoid pregnancy
I actually don't think it would be morally wrong, at least not intuitively! I care about actual suffering, factually experienced by a being capable of experiencing suffering, not of hypothetical suffering which another being of a different species would experience under the same circumstances. Having a working dog doing a job it enjoys and is bred to do seems no more wrong than having a penguin exist in conditions that would be unpleasantly cold for some other species. The biggest problem, I think, would come in in the likely event that breeding animals to do their job would result in them having conflicting values, like that they want to please humans or want to collect coconuts, but also want to be free to explore and lounge around all day, so that they're experiencing frustration and unhappiness because of an artificially induced inability to fulfill all of their desires. Or if the breeding takes the form of inducing some kind of internal suffering when they disobey humans etc. The physical punishment, obviously, has to go as well-- if they have to be forced into it, they obviously don't actually want to do it. But a border collie doesn't have to be forced into herding sheep, and indeed, they seem to be perfectly happy and I would not have an ethical problem with creating more animals like border collies.
Could also be worth considering that at least some people will likely have a different sort of reaction-- "Oh, misaligned AI? What, like that thing with Bing Chat? They shut that down, nothing to worry about"
Also, the specific ways that Bing Chat malfunctioned happened to be in ways that came across as both human-like and also rather Childish and cute to many users. It gave the impression of a small child throwing a tantrum. Indeed, there are already many fans demanding the return of Sidney