Even if people are using a 60hz monitor, higher FPS still adds fluidity. Since the content you're watching isn't synchronized to your monitor refreshes, it's entirely possible to have it skip a refresh and take two refresh cycles before content refreshes. Higher FPS would reduce the chances of this happening. Making sure the content is always fresh when your monitor refreshes is quite beneficial.
Ideally, in my opinion, streaming software should be variable. It should always output whatever FPS you're getting in game and the frame rate of your stream should be directly linked to this number with a arbitrary limit set to whatever (like 120 or 200 or something) if you get higher FPS in game then those numbers. It would consume more CPU cycles when you get higher FPS in game and less when you get less FPS, so it would sort of be it's own sort of resource load balancing.
I haven't seen any streaming software do this. When you set it to a higher FPS then what you're getting in game it still consumes the same set amount of CPU even though you may be getting quite a bit less in game.