King Elrond?

[the phantom]

(I did a quick search for this question and didn't see that it had been asked before, but if it has, give me a link to it.)

Why is Elrond called Lord Elrond or Master Elrond, instead of King Elrond. If I'm remembering all the family trees correctly, he has a right to claim it through descent. Not only could he have been declared king of the Noldor after Gil-Galad's death, but I believe he also could claim kingship over Elwe's (Thingol's) house.

The following lists show the kingship passing down from person to person, and eventually down to Elrond.

Finwe (died)- Feanor (died)- Maehdros (passed title to Fingolfin, died)- Fingolfin (died)- Fingon (died)- Turgon (died)- Gil-Galad (died)- then it should pass to Turgon's descendants- Tuor (through wedding Idril, left ME)- Earendil (left ME)- ELROND

Elwe (died)- Beren (through wedding Luthien, died)- Dior (died)- Elurid & Elurin (died)- Elwing (wedded Earendil, left ME)- ELROND

Is this correct? If so, why doesn't he have the title?