Many people would rather watch movies or plays than read books. This means that for many, the act of adapting these books into a form that people can watch instead of read will expose many people to great works of classic literature who otherwise would never have known anything about them.
Yes, I think that there is a reason that plays are made today from books that were written long ago. Whether it be just entertainment or bringing up a past public problem that is now relevant today, plays that are adapted from books from long ago have a purpose to society that I believe is of importance.
Yes, a play adapted from a book written long ago can be good. There are plays sourced from old books, movies, and even songs. Just recently I saw a play adapted from Harper Lee's "To Kill a Mockingbird." It was terrific. Limiting oneself to only plays that originally designed as such is very limiting.
What makes a play "work" well is often exactly what made a book work well that was written a century or more ago. The examples of successful plays that were adapted from classic books are manifold - "Great Expectations", "Moby Dick" and "The Little Prince" are all excellent examples. These books, written at a time when longer, more verbose prose was appreciated and desired, provide the ideal foundation for the stage. The level of detail of, say, a sunset or a conversation between characters is generally much higher in books written before television, social media or mobile phones and this translates well to visual representations on stage.