I don't think there is any way, or value to be blunt, to answer this correctly.

Bands like The Beatles and Nirvana weren't really viewed as visionaries, or pioneers, or really anything beyond the new "thing" during their time. Heck, the year Abbey Road came out, Sugar, Sugar was the #1 song. Everyone ragged on Paul McCartney's solo music as the worst thing ever made. And people thought Beatles For Sale was going to mark their downfall.

People familiar with Grunge knew that Nirvana was nothing special, they were just a streamlined and radio-friendly Mudhoney. The real visionaries like Mother Love Bone, Tad, and The Melvins never achieved near the level of fame. Similarly, a lot of the "trailblazing" The Beatles were credited with had been done by Zappa beforehand. Remember, Freak Out! came out before Sgt. Peppers.

And to take it back even further, the common people weren't listening to Mozart or Beethoven, that was the music of the very upper crust of society. The common people were more likely to be entertained by local minstrels or vaudevilles (which admittedly Mozart did participate a in a bit). But because there was so much money thrown at Mozart and Beethoven their works survived and were preserved. This isn't to say they aren't amazing and groundbreaking artists, but they were a huge outlier in a world of a very different kind of music. "Classical" (to keep it simple) was never the common and general style of music.

So which artists will be remembered? The most popular who can be easily tagged onto a movement. I love Kanye, but I imagine he'll be tagged onto the Alternative Hip-Hop movement that toppled Gangsta Rap in the early 00's. He didn't necessarily trailblaze, but he was original, fresh, and most importantly, insanely popular. Similarly, Jack White, while not really doing anything new or very special, will likely be tagged as popularizing the Garage Rock revival.

tl;dr: it comes down to a combination of popularity and timing. If you're popular enough at the coming tide of a new sound, you'll be remembered.