Do humans have an obligation to maintain domestic species even if we no longer find them useful as domestic species only exist because they are or were useful to humans? Humans may have different obligations to domestic animals than we have to wild animals.

I and probably the vast majority of people on this planet believe that a child has more rights than, for example, a chicken no matter how humanely we decide to treat that chicken. The operative word here is "humanely" because humans are the only species on earth with the ability to consciously decide how to treat a different species.