I only got into Game of Thrones after it concluded, so I knew how popular the Jaime/Brienne ship was. I was surprised by how cold it left me, for exactly the reasons you describe. I found their relationship quite fascinating because it felt so unique. Not precisely friendship or love as is usually depicted. Trying to describe it leads me to words like "honor" and "obligation," which sound very cold to a modern ear. I thought it was one of the best relationships on the show precisely because it was so hard to define (at least until the final season, but I didn't make it that far).