The issue at stake, is that unless you also engineer them to be similar in every aspect (looks, intelligence, physical capability), there will be differences, and those differences will enable a new hierarchy, with people who have more, and others who have less, thus recreating a unequal base situation.
You don't get to solve the problem by making every human's base situation identical, you solve it by making the inequality device and the means to use it available to everybody.
Some people can just lift more stuff than others, or think about numbers faster or whatever happens to need to be done and their labor is more valuable because it's more efficient. Therefore inequality.
The result is that Americans are just broadly doing worse, because our social system is irrational.
You are right that there are difference built-in to humanity, but we have already overcome those with fairly common technology already. Now inequality is more about who your parents were instead of where you are born or other purely physical problems.
We can ship drinking water to anyplace on the planet. We just aren't incentivized to do so. The person leading a team building the roads that will support that effort could be a wheelchair bound parapalegic.
Our systems don't need to be perfect they just need to be better than they are now.
You make a great point here, and one I hope you continue to push for. Statements like Why must inequality be forever? will obscure this point as it doesn't include the nuance of "not perfect, just better". You will always find people who will argue that "Why must inequality be forever" is naïve at best, needlessly preventing you from finding solutions you might agree on.