On the micro-economics scale, I would not only agree with you, but argue that a successful society depends on it. Just as you should be allowed to participate in whatever harmless recreational activities you like at your own home, so should you be able to keep for yourself anything you've made or earned. Without these freedoms, people lose their incentives to be productive members of society.
However, this breaks down on the macro scale when feedback loops get out of control. Monopolies, duopolies and the like are pretty accepted as bad for economic growth because they have the resources to crush competition and have total control over markets. But monopolies are often just the result of a company that was first to market, had economies of scale, entrenched themselves through legislation, maintained an established brand, and had other feedback loops to strengthen themselves.
Just as we break up monopolies to give competition a chance, we should be working hard to break feedback loops that enforce hierarchy of classes so we can give everyone a chance to be successful or fail on their own.
The parent comment is correct that genetically engineered babies would likely be a mechanism for the socio-economically powerful to entrench their status further. It's not necessarily an argument for outright banning CRISPR babies, but giving more power to rich families absolutely does harm poor families by putting the poor families at a competitive disadvantage.