I think it's stupid, and doesn't make sense in Star Trek. It made sense in IV because of the time travel, as you said. The idea of Multi Billion Dollar corporations still plugging away in the 23rd century does not fit with Star Trek.
Actually, in the 23rd
century, it makes perfect sense. The whole "moneyless society" thing didn't come along until TNG. Yes, Kirk said in TVH that they don't use money in the 23rd century, but TOS was full of references to money and capitalism -- Harry Mudd and Cyrano Jones as businessmen/traders, the "rich lithium miners" in "Mudd's Women," credits as a unit of currency in "Catspaw," "Mirror, Mirror," and "The Trouble With Tribbles," Kirk telling Scotty he'd earned his pay for the week in one or two episodes, Kirk saying in "Errand of Mercy" that Starfleet had invested a great deal of money in his and Spock's training, Spock in "The Apple" reporting just how much money they'd invested in his training, Flint in "Requiem for Methuselah" and Carter Winston in "The Survivor" described as having great wealth, etc. There's no question that capitalism was alive and well in the 2260s. The most logical interpretation of Kirk's TVH line is that they don't use currency because they've switched to a purely virtual/electronic credit-based system -- as we increasingly have today with things like credit cards and PayPal.
Don't forget "Devil in the Dark" in which the struggling miners look forward to striking it rich after they team up with Hortas. I can't remember the exact line, but Kirk says something like "Sounds to me like you're all going to be very weathy men!"
The whole money-less thing is a TNG conceit that really can't be retconned back into TOS without a lot of torturous mental gymnastics . . . .
As for the Beastie Boys . . . hey, it's good to know that the people of the future don't just
listen to Gilbert & Sullivan and classical minuets. (Or, I suppose, Argellian belly-dancing music!)
More importantly, it was a fast-and-dirty way to establish that this Star Trek was a bit more rock-and-roll than the last few films. Which was a good thing.