Inbreeding, as was pointed out several times upthread, causes health issues - not just genetic disease due to recessive genes, but also immune-mediated illnesses, reduced fertility, reduced litter size, possibly a poor immune system, more ill-health and a shortened life expectancy. I'm not an expert, but given the close line-breeding, use of popular sires and genetic bottlenecks that have afflicted almost all breeds, I'd be very surprised if many breeds have dodged all of those bullets.
It's bloody obvious, in fact, that some of them haven't. Flatcoats, for example, are cancer bombs. There's no health test you can run on sire and dam to mitigate that. Dobermans are going down a hole with cardiomyopathy. Wolfhounds - very prone to cancer and various other nasties, many of which can't be tested for (likelihood of bloat, for example). These three breeds have high rates of inbreeding. Some breeds buck the trend, but most don't.
If I wasn't so picky about the traits I want in my dogs, or if I was able to find responsibly-bred crosses of similar breeds, I'd quite possibly be in the market for a cross-bred too. If inbreeding is OP's concern, I can 100% see where she is coming from.