If you use the "right of first born as your criteria then absolutely no judgement is needed. First born is the king. I again point out that
Feanor made
the Silmarils for himself. He lusted after
Galadriel and according to some texts in HoME sought to capture the radiance of her hair co-mingled with the two
trees. I again point out that
Finwe had given up his "claim" to the kingship of the
Noldor by accompanying Feanor into his exile. Both Finwe and Feanor "abandoned" their people by their actions.
Fingolfin, on the other hand was both honourable and loyal.
Finwë had not given up his kingship of the
Ñoldor, he simply holded himself "unkinged" while accompaning
Fëanor in Formenos. If nothing had happened, then Finwë would have returned to
Tirion and assumed his kingship of the Ñoldor.
Note that Fingolfin is not as honourable as you would make us think. Remember that it was Fingolfin
the one who spoke against Fëanor in the Council without the presence of his brother.
Remember that while Fingolfin said to Fëanor that he will lead and I will follow, when Fëanor spoke in Tirion after the death of Finwë, there was almost a battle between them. We have to note that Fingolfin indeed followed Fëanor afterwards.
As you point out, Fingolfin never chose to assert a claim to the Kingship because he was such a loyal son and brother. These characteristics are what make him so attractive as a character and is why so many of his people were drawn to him and refused to follow Feanor. They saw Feanor's heart... and it was cold.
This is both right and wrong.
We can use
The Silmarillion account or the
Shibboleth.
In
The Silmarillion, it is indeed true that it is not mentioned that Fingolfin asserted his claim to the Kingship of the Ñoldor, and that it was his desire of not wanting to leave his people that drove him to follow Fëanor. (and his oath to his brother too).
In the
Shibboleth of Fëanor, Fingolfin did indeed claimed the kinship of the Ñoldor and he even changed his name to
Ñolofinwë.
From the
Shibboleth of Fëanor
Fingolfin had prefixed the name Finwë to Ñolofinwë before the Exiles reached
Middle-earth. This was in pursuance of his claim to be the chieftain of all the Ñoldor after the death of Finwë, and so enraged Fëanor that it was no doubt one of the reasons for his treachery in abandoning Fingolfin and stealing away with all the
ships.
As to who of the two had the best claim for the Kinship, it would have to be Fëanor on the grounds that he was the eldest son, yet it was his own actions before and after his banishment that harmed him. Fingolfin's position as the ruler of the Ñoldor in Tirion could not be supplanted by Fëanor, although Fingolin only became the King of the Ñoldor after the death of Fëanor.
What about the Oath of Fingolfin to Fëanor?
One might wonder if the fact that Fingolfin swore to Fëanor that he will follow him does not in fact would account to Fingolfin accepting Fëanor as the King of the Ñoldor.
The most simple answer would be yes, but one has to remember that when Fingolfin swore that oath, neither of them would know that Finwë would die. Also that this was a unique situation. No one had ever died (destruction of the hröa) in
Aman, and certainly there were no other half-brothers either.
So, IMO, when Fingolfin decided to follow Fëanor he kept his word.