There’s nothing sinister at work. It’s standard practice to fly Old Glory at all but one of the properties you mention. Caesars Palace doesn’t not display the flag out of a misplaced allegiance to the Roman Empire, but because ownership groups have come and gone -- and never seen fit to install a flagpole.
Bellagio has flags flying in the Conservatory, at the employee entrance, and at the marquee, we were assured. Stella Moon of Caesars Entertainment told us, "The flag at Bally’s is flown every day -- with exception of very windy days. Paris currently displays nine American flags in front of property. The Rio All-Suite Hotel & Casino flag is up but it is normally lowered when we get high-wind warnings." The day we wrote this answer, late last week, we happened to notice on our way to work that there were flags flying at both the Rio and Gold Coast (though none that we could spot at the Palms). So our best guess is that your visit must just have coincided with some inclement weather, as there appears to no be dearth of patriotic spirit among casinos.
