I don't know why people think Vulkan will run on OpenGL 1.1 hardware. Desktop wise, the only drivers for Vulkan
right now are Nvidia 6xx+, Intel 5th Gen+ (Broadwell and up), and AMD (I didn't realize they supported this large of a range of hardware) actually goes back to R7 200+, including a fair amount of APUs.
The one benefit that stands out to me if SFML were to use Vulkan is easier use of SFML in multithreaded applications (not just multithreaded drawing, loading of graphical resources on a different thread would be easier).
However, SFML wants to support older hardware and OSX. Apple does not support Vulkan. There is a Vulkan wrapper around Apple's Metal in development, but that's it (for now at least).
In addition, using Vulkan would incur a lot more work for SFML devs. For instance, a
hello triangle sample is almost 800 lines (it does include code for running on multiple OSs, but that's still a lot compared to OpenGL!).
Unless SFML's goals and ideals change (I doubt it, nor would ask for it), I don't think Vulkan-backed SFML will bring more pros than cons
right now. Maybe once Vulkan has matured a bit, and the drivers actually leave beta, it may be worth looking at again.
Also, given that SFML tends to be used by newbies or those who want something that just simply works to get something working quickly, Vulkan doesn't bring much benefit there either.
Yes, Vulkan is a great thing, and very cool. I'm starting to play with it on the side. For SFML, I don't think it's a plausible option yet.
EDIT: I guess I just basically restated what has already been said. Oops.