There's a number of counter examples showing preferences in dittos, but I don't think I've seen this counter example:
I main Samus, and naturally I run into a lot of Foxes. I've seen two general Fox strategies against my Samus:
Until I know which strategy the Fox prefers, I don't have a game plan for what to strike. If I can get it down to FD and Dreamland and get the right one, it is a huge advantage - or if I get the wrong one, a huge disadvantage.
If I win the RPS and go first, I strike something other than FD or Dreamland.
If I go second....
Average those out and it's non-trivially beneficial for me to go first. In my experience winning the RPS has been non-trivially important against every Fox whose style I don't already know. Given how popular Fox is, this happens a fair bit.