I don't think we will converge that much. Most gene differences are insignificant. Is it better to have black, or white skin (or any other skin color)? There is a lot of baggage associated with that question, and some people will make a choice - but not everyone will make the same choice (in a culture I would expect everyone to make the same choice, but other cultures will choose differently), and many people won't care.

There are some genes that I expect to be edited out. I'd give a lot to have the gene causing my high cholesterol edited out, as would my insurance company - the drugs I'm taking are not cheap. There are a number of other conditions that are genetic (and still more that science believes are genetic even though the genes haven't been found). This convergence is good though as these are genes that if you have are known bad - just not bad enough to prevent reproduction.