Sure it is a good prior, I don't disagree with that; however, a sample over many coin flip would actually give you a distribution of loaded flips. Which we could use to estimate the population mean, which is still loaded. This is important, as we need to remember this is not truth. When people mix up truth and science, it stops being objective.

I don't think that real fair randomness actually exist. Maybe you view that as trivial, but I don't.