The issue with labradoodles isn't that they exist or that people have them in itself.
Most people don't care what breed someone else's dog is or what cross for that matter (though there are ethical issues with some breeds IMO and some crosses don't make fantastic pets).
It's that there are ethical issues with breeding, good breeders of any kind of dog breed for a reason, to fulfil a certain role or to create a better standard of working dog or a dog that fits the breed standard and has parents that have been judged good examples of the breed.
They carefully pick the dogs they are breeding, including travelling abroad or importing semen to get the best dogs for the purpose that's wanted and compliment the bitch's traits and come from a different gene pool.
They do extensive health tests, usually more than just the ones the kennel club reccomend for those breeds.
They breed to get a better puppy or puppies for themselves and sell the others to carefully selected owners on the understanding that they are not bred from without fulfilling the same criteria they would apply, that puppy owners are expected to stay in touch and if anything ever happens that means the puppy has to be rehomed the breeder will always have them back - at any point in that puppy's life.
They invest a lot of time and money trying to breed healthy dogs that are fit for purpose and never add to the rescue problem that exists. It is not a profit making exercise, it's an expensive hobby...after paying for a stud, health testing and raising a litter if nothing goes wrong medically and they have a large litter there may be a small profit, but it's more usual to just about break even, any medical complications mean it costs money.
That applies equally to all breeders, so, it is possible to have good ethical breeders of crossbred dogs...but, they're very few and far between.
Rescues are full of thousands and thousands of dogs of all breeds and crosses who people bred for no good reason and they carry on doing so because people give them money for doing it.
Labradoodles have very little purpose, a very very small amount of them may make non-shedding guide dogs, most aren't reliably non-shedding and aren't temperamentally suited to it, there isn't a huge reason to breed them for that as most guide dogs are purpose bred at the guide dogs breeding centre from carefully selected parents.
They don't make better retrieving dogs than poodles or labs, they don't work better for any other activity.
Yes they're nice pet dogs...but so are most dogs, including the rescue dogs that wouldn't exist if people were pickier over who they gave money to for puppies.