They may not sing about it, but they would still know. This defeats the purpose of Gondolin being the first place where Balrogs are defeated by Elves.Well, this is why I had suggested Aegnor flying into a rage, slaughtering a bunch of Orcs and earning a mutual kill against a Balrog; nobody likes to talk about it the same way nobody sings of Fingolfin’s duel with Morgoth. A company of angry Elves at the Nirnaeth Arnoediad (the Elves from Nargothrond led by Gwindor) slew hundreds of Orcs (including a decoy army?) and got all the way to beating on the doors of Angband before they were all killed except for Gwindor, who was captured.
Even then I would prefer for Ecthelion to be helped by the hallowed fountain of Ulmo, whilst Glorfindel sheer desperation and love for Idril's family makes him win an impossible fight.