Galadriel... High Queen of the Noldorin Elves
 

Since she's the highest remaining Noldorian royal, wasnt her right the one to become High Queen of the Elves (all in M.E.) and High Queen of the Noldor?

Same reason Elrond wasn't the High King... I simply don't think there were enough Noldor left in Middle-Earth after the Last Alliance to warrant a regal title. There's an interesting thread on this here.

She could have been...