I suspect that you have objects of sentimental value as well. Most people do. Perhaps it is a book given by a friend that you don't throw away, even though you never read it and, if you had to, could replace it for a few dollars. Perhaps it's an autograph from a celebrity, or a prop from a movie.
Sentimental value isn't rational, but it's innately human, and practically all people practice it. The art market in particular is famous for expanding it to some ludicrous levels, where sentiment is given a dollar value in the seven and eight figures, but it's mostly just rich people playing on exactly the same emotions you have, with more money.
It's complicated by additional factors of competitive culture and possibly some money laundering, but at the base of it is a feeling that a piece of art that "witnessed" history takes on a value beyond the visual conveyed on the canvas. Often, the artist was innovative in some way that's appreciated by fans, and that innovation is no less rational than a baseball that was hit out of the park at an important time -- even though it's just a baseball.