Fingolfin had
some hope, as we have of gaining the lottery prize
He could strike gold, even if the chance is beyond calculation.
Finrod's deed, on the other hand, could accomplish
nothing -- he would simply postpone
Beren's death by his sacrifice. Who could imagine that
Lúthien, of all people, would come to the rescue?
(as you see, "Finrod's deed" for me is not just going on a secret mission, it is particularly his last sacrifice exposing himself and fighting
Sauron. Even if he won, he would still be a prisoner, and he would still be killed. Sauron was just "playing with him", as it is)