I guess that whether or not the light novels are "good" depends on what you like. Kawahara Reki (the author) became a much better writer over time, and I think the latest light novels are higher quality than the earlier ones. In that sense, the newer arcs are worth reading, especially since they haven't been made into an anime yet.

That said, I think I enjoyed the anime more overall, especially the first arc of season 1 (part of which was based on the manga, not the light novel). Since the series is so popular it seems almost inevitable that they'll make the Alicization arc into an anime, so you could wait and watch it then.

And since you're an Asuna fan, I'm not sure how much you would enjoy the latest arcs. Without spoiling anything, I'll say that Asuna basically disappears for several books. She does come back later, though.