There is nothing intrinsically wrong with crossbreeds, but you shoul demand the same from their breeders as you should from a pedigree - health testing for the known problems in all breeds that go in to their make up, and that they are bred in excellent conditions from dogs that are healthy, of good temperament and look like their breed.
Unfortunately, most fashionable crosses are bred in unsavoury conditions, bred to excess, often without any health testing at all.
Breeders are also very clever indeed at putting a respectable veneer on their behaviour. Don't be fooled by posh websites. If you come across any kennels that advertise several breeds/crosses, start by asking their council how many breeding bitches they are registered for, you will often be shocked.
All dog buying is difficult these days. For my money, the most accountable way is to find the right breed and then find the right breeder - whether you are interested in showing or not (most aren't, no worries), a show breeder is the most 'accountable' you are likely to find. You can track how much they breed, you can evidence health testing, you can be reasonably sure that if they are successful their dogs have decent temperaments or they'd be unlikely to do well in the show ring.
Obviously there are exceptions to all of these, life's like that. However, the only way I would touch a crossbreed with a bargepole would be if I had a very close link to a breeder who health-tested, and who you know is telling the truth on number of dogs/litters.