Can you share a source for that? I know at least 1 person first hand who has renounced and then later on in their life regained citizenship. It's possible the rules around this have changed however.

Yes, I think the rules might have changed. Apparently nowadays you can regain it "under very limited circumstances": https://www.usa.gov/renounce-lose-citizenship

When did the rules change? You may have just been mistaken. I thought it was always possible to gain citizenship again, assuming you're eligible like anyone else and are willing to go through the normal citizenship process.

Are you saying the immigrant visa path isn't available to former citizens? That seems surprising.

Sure, it's a very difficult path in practice... But in theory I don't see why something like this wouldn't be possible: you renounced your citizenship, win the Nobel Prize 30 years later, get an EB-1 visa based on that achievement, then get naturalized five years later.

There have been (so far unsuccessful, but possibly successful in the future) attempts to ban US citizens who renounce from ever stepping foot in the US again.

> (E) Former citizens who renounced citizenship.— Any alien who is a former citizen of the United States who officially renounced United States citizenship is inadmissible. https://en.m.wikipedia.org/wiki/Reed_Amendment_(immigration)

This is banning reentry for those who have stated their reason for renouncing is due to tax avoidance. When I renounced I began telling them it was due to tax compliance, and they were very careful to not let me say tax avoidance. It is completely different. I’d be happy to pay an a amount to the US for citizenship every year but can’t deal with the thousands I pay accountants and the days I spend compiling and working out amounts for the calendar year as opposed to the Australian financial year. Also the anxiety over the ever changing laws and fines.

This reentry ban has never been enforced but could be in the future, if anyone has actually been able to say they renounced due to tax avoidance.

Yes, the Reed Amendment as passed is as you describe. However, see the section in the linked page on the SAFER Act.