There were many Beastie Boys in Mozart's day and age. But they didn't survive.
I doubt any contemporary musician will make it into the 24th century. Elvis or the Stones maybe, I dunno. But today's classical composers, Mozart, Beethoven et al, will still be there, I believe. Same reason why Homer is still around, altogether with Shakesspeare. Some artist's work survived until now and will survive as long mankind exists.
That said, I find that carriage and classical music comparison justified to show how ridiculous that scene was. 250 years, people. 250 years in the future, after several alien contacts that boosted humanity's development. Kirk lives in a world that uses matter/antimatter reactions, solar energy, fusion reactors. Mankind mastered gravity, so their vehicles are able to fly. If they travel, they beam over thousands of miles or fly shuttles. They are able to turn energy into matter! I think people here watched Trek way too long so they don't realize how advanced that future actually is. It's not about iPhones being better than communicators, that's nothing compared to the rest.
And then again, how many people collect 300 year old carriages?
And moreover, how did he fuel the engine? 50 years from now, oil reserves will be exploited. 250 years from now, mankind will have used alternative energy sources for 200 (!) years. I doubt they will even know what gasoline is. "Daddy, what is oil?" - "You know, son, 300 years ago they burned a black liquid to create energy. And they burned so much of it, their atmosphere was full of toxic smoke, and they exploited all of their reserves of that raw oil. Only then they were forced to use the energy of sun, wind and water." - "Sounds like the stone age."
Kirk using a bike with wheels is already borderlining stupid when we've clearly seen what kind of bike the police uses. Oh, the wheels where magnetically propelled. Big deal. Other bikes are propelled using anti-gravity engines!
