Let's say 100,000 years ago, a small group of humans left Africa for the other places of the world. That small group of humans represent a very small fraction of genetic diversity--it's effectively genetically identical. Assuming no more admixture over the millennia, the out-of-Africa humans will get more genetically diverse. But so are the original Africans, who also have the genetic diversity they started with--they're getting diverse no less quickly than the out-of-Africans, and since they started more diverse, the entire out-of-Africa can't ever catch up.
Real genetics is of course more complicated than this simple picture, but the basic principle holds that you find more diversity the closer you get to the origin.
Same for humans during migrations. Only a small percent of humans left Africa, and then only a smaller percent kept going, etc. So as long as not much time has passed to generate new variation in the areas they settle, only a small fraction of local variation ever leaves is low. And that's what we see, Africa is extremely diverse, Europe/Central Asia less, east Asia even less, etc. It's neither bad nor good, just a number.
There are some other factors, such as mixing with people already present at the destination for a long time (Neandertals, Denisovans) which balance it out slightly.
The US has lots of diversity, but there were a lot of groups in Africa for a very long time (maybe 10k+ separate groups). It's unlikely that people from each one have made it here, or even out of Africa at all, in significant numbers.
There is also some immigration directly from africa, but that can only increase it to at most the same as exists there. Almost certainly somewhat less, in practice.
cough mysterious 1:4:9 monolith cough
I've heard that humans were at some point reduced to a very small number, like thousands of individuals.
So how did a few thousand individuals become such great genetic diversity? Does genetic diversity come from being isolated, instead of mingling with other migratory groups?
There is small amounts of "multiregionality" since some peoples are part Denisovan and most everyone is part Neanderthal, but it's not even a plurality in anyone we've ever found.