The crusaders of 1204 are able to take all of western Asia Minor and the Nicean state is never established. Do they retain Asia Minor until the Mongol invasions or do the local Greeks rebel?
Um... Dunno about the Greeks, but the Turks will certainly have something to say eventually. More Latins in Anatolia mean less concentration on Crusader States means potentially more powerful Egyptian/Mamluk/Caliphate-esque state to oppose the Mongols when they arrive.
In the end, I would expect something similar to OTL, but perhaps instead of an Ottoman-dominated Egypt, we have an Egypt-dominated Anatolia. Maybe... maybe not. All things flow and change, so hell, could be that without the Crusaders to deal with so much, the Egyptians become hedonistic and lazy and the Mongols overrun the Levant, Cairo, and all of North Africa.