The end provides a decent summary of the article, and how I've tried to think about things since I first read it:
"It's sad, but it's also ... great, really. Imagine if you'd seen everything good, or if you knew about everything good. Imagine if you really got to all the recordings and books and movies you're "supposed to see." Imagine you got through everybody's list, until everything you hadn't read didn't really need reading. That would imply that all the cultural value the world has managed to produce since a glob of primordial ooze first picked up a violin is so tiny and insignificant that a single human being can gobble all of it in one lifetime. That would make us failures, I think.
If "well-read" means "not missing anything," then nobody has a chance. If "well-read" means "making a genuine effort to explore thoughtfully," then yes, we can all be well-read. But what we've seen is always going to be a very small cup dipped out of a very big ocean, and turning your back on the ocean to stare into the cup can't change that."