I can't speak for all servers, but the situation in Cornelia (at least, during JP primetime and for the JP population) is quite the opposite... it is in fact the party search function that is used more often compared to that of the player search function in order to form parties.

How it works:

Party leader sets up what s/he wants for party.
Shout in Ul'dah, advertising what the party is for.
Wait for people to join.
Party.

Moogle/Ifrit parties formed through this method fills up extremely fast.

It's probably the reason why the NA population have it so difficult in Cornelia... they are still too used to the FFXI 'invite' based parting system and are not aware of how parties are formed in FFXIV.