[sarcasm]Hopefully this name problem wasn't a cause for their decision to absorb US Air and change the name to US Airways.[/sarcasm]
Could it also be that the Cactus and US Air planes have different liveries still? It'd make it easier for other airliners to understand ATC controls when they get sequenced behind a "USAir" painted like a USAir than like a "Cactus", and vice verse. (Kind of like you still hear pilots told to follow the Song colors).
As with Delta, I agree that history as something to do with it:
They've been around since 1928 (thanks wikipedia), so they were probably calling themselves "Delta" over the radio long before the IATA formed the first form of the military alphabet we know today (proposed on 1951, implemented in 1956, universally used by 1959, thanks again wikipedia). Plus who knows when airports got so complicated and busy that specific taxiway instructions needed to be given on the ground using alpha, bravo, charlie, delta, etc.? (someone write a wiki if you know