Bloodlines

[Guinevere]

Well, I think "blood" is just used as a metaphor for what you inherit from your ancestors... So it's irrelevant whether Melian as a maia had actual blood. (While conceiving and bearing her child she certainly had a body) . And I am sure she must have passed on something to Luthien.
And of Aragorn, Legolas said:

...for is he not of the children of Luthien?Never shall that line fail, though the years may lengthen beyond count.

For Tolkien this "bloodline" seems to have been very important!
in letter #144 he wrote

...the Elder Children, doomed to fade before the Followers (Men) , and to live ultimately only by the thin line of their blood that was mingled with that of Men, among whom it was the only real claim to "nobility".

In Elrond (and Elros) the lines of all the Elven houses (Noldor, Vanyar, Sindar) come together as well as the lines of all 3 houses of the Edain (Beor, Hador, Haleth) (plus the Maia strain from Melian) And in Arwen, there is in addition the line of the Teleri of Aman (through her mother Celebrian)
I'm sure this is no coincidence!
Because of Arwen's marriage to Aragorn the inheritance of all this nobility will live on in Men.