Readers DO judge a book by its cover. An important part of our job is to connect readers with materials that make them want to read MORE! Books that are in disrepair or that look like something your grandma would consider an antique, aren't motivating anyone - but especially not to today's young readers.
An old, irrelevant and out of date collection sends the message that we're all of those things too. Our collections are a reflection of what we value and are about. I'd rather have just a few shelves made of awesome than thousands of titles that send the message that my library is still in the dark ages. Holding onto dinosaurs will only make some folks think you're one too.