In fact, given the number of Apollo missions, there should be half a dozen or so flags on the moon now, making its surface more visibly American than a NASCAR race on Independence Day.
But Actually ...
According to Buzz Aldrin, he and Neil Armstrong accidentally placed the original American flag too close to their spacecraft, and when they took off, the flag was blown away. Whoops.
The film crew was already on overtime, so the director decided to wrap instead of shooting the scene again.
It's true that subsequent flags planted by astronauts are still standing, but the message we're sending out to any passing aliens is less "America, fuck yeah!" than "WE SURRENDER."
Which is to say, they're not American flags anymore, just hunks of white cloth. You know how dye tends to fade in the sunlight, like when depressing old video stores used to leave their movie posters in the window too long? Well, when you leave fabric outside on a barren space-rock without the protection provided by the atmosphere, it fades even quicker. All the American flags lost their colors a long time ago, and are now a surrender-friendly shade of white.
NASA via Gizmodo
"Look! The Earthlings are displaying the white flag of war! Man your battle stations!"