Clearly It really had nothing to do with inbreeding so much as pride. Being proud of having a house elf and a successful house elf lineage serving a proper pure-blood house. They grew too old to carry tea, and something had to be done. It also allowed the house elves to continue to serve a house even when they were incapable of literally serving by providing the house with another piece of them. They were a trophy, a piece of art, prestige, and a symbol. I'm sure you'll just dismiss that as a result of inbreeding, because you strike me as the type to always need to be right but that's just how it was when it was started by Great-Great Aunt Elladora, whose parents were not related closely enough for inbreeding to be a factor (unless you're counting "we're all human" or "we're all humans with magic from the same source" as a factor, which I'm not because that'd just be silly).