Most Americans that live overseas tend to be expats rather than immigrants. Those two terms don't convey the same meaning.
Technically of course you are right.
Practically, they barely pay anything significant.
The lower net salary in Europe / Asia associated with rather high local tax means that most Americans citizens oversea barely own anything significant back to the state.
However it does remain an annoyance to fill the tax declaration every year: I know several American who chose to give up their citizenahip just to avoid this specific issue.
If you are normal wage slave with limited savings then yes the exclusions mostly work.
The 2026 Foreign Earned Income Exclusion (FEIE) allows qualifying U.S. expats to exclude up to $132,900 of foreign-earned income from their U.S. federal income taxes. Married couples can exclude up to $265,800 if both spouses work abroad and each meets the eligibility requirements.