Yes, we can eliminate many classes of disease with genetic engineering. But as you allude, it won't stop there. People will pick and choose external characteristics for their children. The idea that doctors will somehow be able to keep this in check is to ignore history and the huge incentives that are set up here. First, it will be diseases. Then it will be, for instance, the genetic propensity to obesity. Then 'disadvantages', like being too short or a little too dull. Then it will be external traits, like blue eyes or blonde hair. Then it will be mental traits and personality characteristics. And where it will end will be totally inhuman and beyond our present comprehension.
The result will be massive suffering, inequality, and possibly even the extinction of humanity as human genetic diversity is replaced with an ever-accelerating social competition that ends in a monoculture that will probably be ill-suited for survival the same way modern dog breeds often end up unsuited for survival.
Yes, it would be lovely if we could use genetic engineering technology safely and responsibly. We can't. That's to say nothing of the risks inherent in the technology if it became simple and cheap for anyone to use even on non-humans.