I think there's a couple of issues with the keep it secret, keep it safe line of thought to gene editing. If this stuff is possible, it seems inevitable, and not just because some rich fucks want to enshrine a permanent caste system. Eventually people will gene edit their children even with the best of intentions and then the cat will be out of the bag. Even if you decide to kill everyone that does it, it won't be easy to do so since, well, the elites of society are the elites for a reason, and they already break laws all the time for all sorts of shit, they'll absolutely uplift their children if possible. Secondly the only people who are going to have the means and motive to keep gene editing secret are... going to be rich fucks who want to enshrine a permanent caste system. Not to mention that currently human society is too fractured to create rules stopping things from happening. What if, say, the EU makes laws restricting the creation of genetic supermen, that's all well and good for the EU, but then the elites of China and America go ahead and enhance themselves? Now you still have the problem of enhanced elites, but the side that at least is somewhat interested in equality is at a disadvantage. A hypothetical future society that can draw together to the point where they can totally stop elites from doing shady things is honestly a society that's so far more egalitarian and unified then our own that it probably can realistically uplift everyone and so should anyway.
Ultimately, I'm pessimistic about the future, and think that if it is possible to create genetic supermen, it will end up enshrining a caste of elites that lord it over everyone else. But I'd agree that the only way to prevent this from happening is to create a society where everyone can be uplifted. It even flips the calculus of relative advantages that parts of society have over each other, if the EU uplifts everyone, and china and america only uplift the elites, the EU will be way better off and in the long term should out compete the non egalitarian societies