To be perfectly clear. The US has a much higher standard of living than the vast majority of countries in the world and people from those countries hope to improve their lives by moving there.
The US has a lower standard of living than basically all OECD countries.
To use a sports analogy, the US is last place on the pro league ladder, while also being first place on the “everyone else” ladder.
I don’t think this captures the full story. The US has a bimodal standard of living reflected as a lower mean relative to other advanced nations.
It can be simultaneously true that immigrants to the U.S. from both advanced and developing nations both experience a higher standard of living than their countries of origin.
Immigrating to the U.S. with an advanced degree in an in-demand field: you likely will experience a higher standard of living.
Immigrating to the U.S. from a developing country without a particularly in-demand career: you likely will experience a higher standard of living.
Also there is a bit of inertia. In people's imaginations, the US still seems to glimmer, even if the reality isn't the same.