> […] children of diplomats aren't citizens at birth, but U.S. courts have jurisdiction over diplomats for some activities?

AIUI, IANAL, US courts and law do not have jurisdiction over diplomats. When a diplomat the 'hosting' government agrees to immunity, so cannot be prosecuted. E.g.:

> The collision caused diplomatic tension between British and US officials. [Anne] Sacoolas fled Britain soon after the incident, and claimed diplomatic immunity with US support.

* https://en.wikipedia.org/wiki/Death_of_Harry_Dunn

The 'source' country has to agree to remove the diplomatic coverage.