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I don't think you can make a blanket statement about whether you can manage to retain breed traits without damning the dogs.> If you control for #1 and #2 is there still a higher incidence of issues? Probably. Why would reducing diversity be a free lunch?
You just answered your own question. Is it theoretically possible for any species (including humans) to be purebred/inbred while still avoiding the whole host of genetic disorders and health complications? Sure, anything is possible. Is it likely? Of course not. The video does a pretty good job of showing how so many purebred dogs have worse health compared to their mutt counterparts.
You bring up a good point about eating meat. Most of us are willing to trade off animal welfare/suffering for human pleasure and aesthetics, so why not apply the same principle to dogs. One argument is that most people who adopt dogs do so with the genuine intention to love them and care for their welfare/health. In fact, people get so attached to their dogs that they spend a great deal of money to promote their health, and deeply mourn their suffering/death. Given this, it only makes sense for dog owners to adopt mutts.