Interesting question. But the problem isn't just the time period.
Indy was always after the MacGuffin. Even in Temple, he saved the enslaved children as an afterthought. He was really after the stones. Had to rescue Willie and Shorty, but still, the stones played a central role.
No great artifacts in Compton. And if the King Tut exhibit tours again, it won't be going thru Compton.