The fusion of the sperm with egg in a natural process leads to a natural and healthy creature.
Natural yes, healthy mostly.
We only play "god" for couple of decades on genetic level, and will take some time to understand all and improve technics to much or even exceed natural quality.
Nature had almost a billion of years to experiment in sexing department, and still is far from being perfect, in human understanding of this term. It is estimated that about half of all human pregnancies are terminated, by nature, in first month, due to genetic complications of a fetus. One in 5 people or more live all life with some substantial genetic abnormalities (joint toes, week heart, "slow" in school and work, blind, etc) and die prematurely. To be honest I was never impressed much with nature, the blind and not caring "mother nature".
I'm sure that in the future, once we completely understand how it works, we'll be able to improve upon design. And with human genius we can do this in hundred years, in what took a billion for blind nature.
By no means I'm advocating alienating ourselves from nature. We are very in tune with our environment generally speaking, and for our own health shouldn't change it too much. I'm barely musing about improving and perfecting few things, so at the end of a day, we all will be beautiful, healthy and smart.
I'm sure there will be some more effort in the future to bring back some extinct species. Most animals won't survive just because today's environment is different. For example, dinosaurs were used to 40% oxygen (21% today) in denser hotter and very moist air, their plant food source changed too, plus all their digestive bacterial flora (essential to digest food) is gone too.
With the Neanderthals it will be easier because of short time laps since their demise, and earth not changing much since. But they would certainly have a problem adopting to agricultural/industrial way of life, or coping with addictive substances like alcohol and other drugs. Same problems experienced on big scale by aboriginal people of Australia or Canadian prairies, the pure hunter gatherers.
To be honest I'm not looking forward to recreation of extinct species. But I wouldn't mind growing parts of them to see how they look. Let's grow dinosaur skin to finely see how it looked, with feathers or not.
Our genetic knowledge will grow fast, and soon we will be in a position to tell, just by looking at DNA, what the animal looked like, what it ate, etc, without growing it in our labs. We will put DNA into super computer and it could show the full animal, how it moved, or what sounds it made, and see it in 3D.
What about future pets though?
PS. Can you imagine what weird pets people will have in the future, giving the technology? Maybe little griffin for someone, or a little flying dragon? Like T-rex looking lizard?