Additionally, humans FREQUENTLY choose to adopt rather than risk passing on a genetic abnormality to a biological child.
The only difference here is that we would be making the decision for the tigers since, as everyone would agree, they don't have the ability to understand the consequences and make the decision themselves.
1.5-2% of children are adopted in the US. About 50% of those children's parents adopted due to infertility, of which an even smaller fraction is voluntary infertility.
I wouldn't say that is something that humans due frequently, and is probably limited to a small set of cultures, and an even smaller subset of parents with both the knowledge and fortitude to make that decision.
I'm an adoptive parent and know several dozen other adoptive families. I have never personally met someone who chose to adopt to avoid the risk of passing on genetic abnormalities.
Unfortunately, I also know some who chose to ignore the advice of their genetic counselor and now have 3 lovely, but severely mentally disabled children (Fragile X run amuck) who will never be able to live independently.
Same thing has been done with servals ("savannah cat"); I can only imagine how awesome/terrifying it would be with other lesser wild cats, although I think there are enough differences between the great cats and domestic cats to make it difficult/impossible to do naturally (tiger/cat or leopard/cat cross).
So, I think there is a hook. It's just a really shitty one. Note that the hook for dogs can backfire as well, if they try to assert pack dominance vs. their owner. So we breed really submissive dogs.
Tigers and lions are very confident apex predators, so they don't really have the vicious instinct or the intense fear response that some animals have. So they don't deliberately attack humans. By contrast, leopards and jaguars will kill you out of sheer viciousness, bears will attack you if they feel threatened, and polar bears will attack you because they are hungry and you are made of meat.
The main danger with tigers and lions is that they don't really understand how fragile humans are, so they might accidentally kill or maim you, which happened to Roy.