Why not put rods in? They are cheap protection. Two rods and a short length of #6.
Not like what you are plugging in is cheap
So when we did my mobile home many years ago, the electrician put rods in at the service disconnect (in another building) and also put rods at the mobile.
Mobile homes do not get grounding rods (or at least did not at that time) at the mobile home's panel.
Having the rods at the mobile in addition to the rods that were already at the service was a code violation and it did not pass inspection. They could not be there redundantly. (in that inspectors eyes).
So, I wasn't sure about this situation either. I like the idea of having rods but don't want to get failed on the inspection.
Assuming I did have rods though, would you guys also bond the pedestal to the adjacent yard hydrant? I can't fathom any reason too but I am also not a sparky.