Should I rent a 4x4 in May?

Hi everyone! My partner and I will be traveling to Iceland from May 12-21 and we will be doing the full ring road. Since the highlands will be inaccessible, is there any point in renting a 4x4? Will there be any F roads that are open or any opportunities to stray off the ring road that would either require or be made easier with a 4x4? Thanks!