The trap filled tomb did not originate in Indiana Jones, which is a homage to 1930s pulp adventures, and many of the examples in D&D predate the movies, like The Hidden Shrine of Tamoachan, which was published the year before Raiders. They are tapping into the same zeitgeist.
If you look at the specific traps in Last Crusade they are pretty standard. The Breath of God is a standard scything blades trap (kneel for advantage on Dex save). The Name of God is a standard hopscotch trap (for example there is one in Doctor Who: Death to the Daleks episode 3/4 in 1973). Easy to do, you just need your code word and an effect for stepping on the wrong tile. The Footsteps of God is the difficult one to do in D&D, since if the players can't see a bridge across the chasm they will probably bypass it using magic. But there are many other ways to test players' faith. But note that it is famously subverted in Tomb of Horrors, and players may be aware of that.
For clear deliberate references to Indiana Jones in 5e products, the archaeologist background in ToA is the only one I can think of.