So the old movie serials were stereotypical and the new Indiana Jones serials are stereotypical. Nice. You still haven't learned that two wrongs don't make a right.
Old Westerns were based on a formula also: whooping warriors attack peaceful pioneers. Should new Westerns be based on the same formula? Most filmmakers would say no, but if you were consistent, you'd say yes.
Spielberg and Lucas changed the formula enough to avoid showing hordes of black savages in deepest, darkest Africa. And to avoid showing black Uncle Toms and Aunt Jemimas in subservient roles. Only Indians remain as a substandard species.
I don't recall if Indiana destroyed any other artifacts in the series, but he helped destroy the crystal skull. He also helped destroy Indian ruins in two movies. He could've left these ruins alone, but his covetousness outweighed his caution. Apparently he never met an Indian site he liked--i.e., one worth preserving.
Indiana the international thief
More important, what you call "recovering" is what most people call "stealing." Indy stole artifacts from the people who owned them without permission from the host countries. Like a typical Westerner, he considered his wants and needs paramount. The term for him is "tomb raider" or "grave robber," not archaeologist.
I'm not sure we ever saw Indy conducting a proper archaeological excavation. In fact, while robbing Indians of their heritage, he caused the destruction of countless Indian artifacts. This man didn't care one whit about the laborious work of studying indigenous cultures. He was an armchair theorist who supported himself as a procurer of stolen goods.
Critics have made much of the fact that Indiana returned the crystal skull to its source. Supposedly this showed a more enlightened attitude. But Indy still stole something that didn't belong to him.
Recall how he got the skull in the first place. Like a common criminal, he raided some tombs outside Nazca, Peru. He sliced open a mummy and took the skull, a gross violation of scientific ethics.
You mentioned Kennewick Man. If Indy were on that case, he'd stand with the scientists against the Indians. If the Indians reburied the skeleton, he might exhume it again. Whether literally or figuratively, he'd thumb his nose at their "superstitious" beliefs.
Finally, we know that box-office receipts are your sole measure of a movie's quality. No big surprise there. If a film does well, you shill for the people who produced it. Success justifies stereotyping in your white-oriented world.
For more on the subject, see Indiana Jones and the Stereotypes of Doom.
Below: Indy plies his trade as a trafficker in stolen artifacts.