Yes, exactly, it's an interesting point, I remember it coming up in stats class decades ago.

Yep

Assuming the choice is random - no way to track which thimble the pea is under - the odds of the guess have changed from one in three to one in two when tbimble C in revealed, but the odds between the remaining two thimbles are still even so why is changing an advantage?

As I recall this trick from a magic set years ago, the pea was actually slipped under the edge of the cup and palmed when mixing up the thimbles so none of them have the pea under it.