Hey, and welcome
I'm new here too, and I used to think like you. Why not let cats breed? Babies are cute! Then I learned why not.
Firstly, mixed breed cats and dogs do not have 'hybrid' vigor. They are not crossing species. A domestic cat is a domestic cat. It is the same species whether or not its a persian or an abyssinian. They are different breeds, not different species. In order to have hybrid vigor, you would have to cross a domestic dog with a wolf, coyote, or other canid species. To have hybrid vigor in cats, you would have to cross a domestic feline with another species of cat, such as an Amur leopard cat, or a Cerval, or an Asian leopard cat. Not just a siamese to a himalayan. If you breed one kind of cat that is prone to a genetic problem, such as heart disease, to another breed of cat that is prone to eye problems, you are not increasing the chances the kittens will be healthy, but rather INCREASING the number of genetic problems they can have! Now, instead of just being at risk for heart problems, they are ALSO at risk for eye problems.
That aside, you asked if God didn't want them to have kittens why would he have made it happen? Well, he may have given them the functionality to have them, but he also gave you charge over your animal's welfare and wellbeing. To me, saying the above is like saying 'well, if God wanted the cat to have asthma, what right do I have to give it medicine?'
Having kittens is dangerous on the female. They can get infections, mastitis, they could die in labor. Its dangerous for the kittens. And with millions getting killed worldwide, it is plain irresponsible. Cats are not like humans. They don't sit around thinking 'Gosh, I just don't feel complete unless I can have kids to pass my legacy on to'. This is not a choice they make. They are slaves to their bodies. It doesn't matter if a female cat wants to or doesn't want to have kittens. When they go in heat, if there is a male around, they have NO CHOICE. They will get bred, like it or not, and then be pregnant, like it or not.
Mixed cats are wonderful. I own five of them. It doesn't matter to me that they're not purebred. However they are all fixed. Their lives and health matters to me. I don't want my boys escaping and getting into fights, getting abcesses or testicular cancer. I don't want my girls getting infections, wearing themselves out physically producing litter after litter. I don't want them getting uterine or breast cancers, which are virtually eliminated after spaying or neutering.
I have one purebred cat who is 90% likely to be sterile. He will still be fixed, because I do not want the health or hormonal problems putting his life at risk.
Yes, it is okay for responsible purebred owners to breed for very specific reasons. Their cats are health tested and their lines are known. The genetic problems they carry are known, and can therefore be mostly avoided through careful selection of breed partners. The cats usually are not bred unless a home is lined up and available for every single kitten that cat could produce. The breeder usually...and should...use very stringent criteria on selecting the homes for the kittens and will either take back or aid rehoming one of the kittens they sell at ANY point in that cat's life. Even twenty years down the road, if need be. They take full responsibility for every life they create.
Yes, their cats are expensive. This is also for many reasons. They want someone who can afford enough to provide that cat adequate care for its entire life. They want someone to think the decision through seriously (it's hard to make a $800 impulse buy). Plus, they give their cats and kittens the best of care including all shots, check-ups, and genetic testings, which cost more money but ensure you're getting a healthier cat in the long run.
People are more likely to take a cat they spent money on to the vet. Free kittens tend to be ignored when they are sick (TEND to be. I'm not citing every person that owns a free kitten, here). People are more likely to take the time working through any behavior problem that might arise with a cat they spent money for, than for a free one. Heck, cat scratches the couch? Well, it was free. Give it to the shelter. We can always get a new one.
Education is the key. You're dealing with lives here...lives that feel, care, and can get sick and die. Every life you bring into the world is a life YOU made to happen, and one YOU have to take responsibility for. That is why it is only okay for responsible purebred breeders to breed, and not just anyone with a moggie they think is cute and sweet. Millions of cute and sweet moggies get put down every year, as do millions of purebred cats bred by IRRESPONSIBLE purebred breeders.
Research, educate, enlighten. Good luck with your cats, and I sincerely hope you change your mind.