Galadriel was not queen of the Noldor, and she was not Fingolfin's daughter, nor Fingon's sister (she was the daughter of Finarfin and sister of Finrod).
It seems that women were not eligible to inherit the 'kingship' as they were passed over in favor of (younger) males.
It is possible that Elrond did not want the kingship, and any such title would have been purely nominal after the death of Gil-galad. It is also noted in The Problem of Ros in PoME that Elrond actually prefered to reckon his lineage to Thingol instead of Turgon.
It is interesting that in earlier tales it was Elrond who 'ruled in the west of the world', after the overthrow of Morgoth, until JRRT invented Gil-galad.
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Tar-Elenion
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