I absolutely get the Poodle cross love. Bucketloads of them around here, and the majority are attractive little dogs, mostly with decent temperaments, although many are not 'hypoallergenic', separation anxiety does seem to be a bit of an issue, and many owners obviously under-estimate the necessary grooming costs and the fact that they also have to groom in between!
As Bubble2bubble says, crossbreeds of any type are not inherently more (or less) healthy than purebred dogs - it will depend entirely on the health of both parents. It is probably not unreasonable to assume that breeders who are crossbreeding have not chosen the best stock to start with.
Some are properly health tested (which is not 'vet checked'), but not many. However, it is possible to do your homework on this.
Unfortunately - and this is my real issue with the designer crossbreed world - it is inescapably true that the vast majority of 'designer breeds' are puppy farm bred. This is the bit that I cannot stomach, and I'm afraid so many buyers are wilfully ignoring this.
You show me any 'xxpoo' breeder that has a fancy website, and I can bet in most cases they can be proved to be a puppy farmer in 10 minutes. Many that don't have websites and claim to be selling from their own pets I can probably track down that they are a dealer. There are some that are breeding in a good pet environment, but blimey they're few and far between.
Show me any puppy of any breed or cross that has been bred and reared with care and I'll be happy to tickle its tummy and wish its owner luck and love, but I cannot stand the support of puppy farming and the misery it causes.
(Oh and the 'all breeds were crossbreeds originally' point is completely irrelevant to today's crossbreeds. Breeds are developed over many years with a purpose in mind, and with a hard 'stockman' view to achieving what they wanted and to getting dogs that bred true. Continually crossing Breed A with Breed B is not the same thing in any way.)