Byzantine fanatic, could you expand on what you think would happen with a more powerful, longer surviving empire of Nicaea? I'd love to hear about that timeline!
Well, the key would be to ensure that they stay focused on their Anatolian core. In our timeline, they became increasingly drawn into Europe and this over-stretched their resources.
The key turning point is the period 1224 to 1230. In 1224, the rival Byzantine kingdom of Epirus captured Thessalonica. This city was second only to Constantinople. After the victory, it seemed Epirus was the most powerful successor to Byzantium. But in 1230, the forces of Epirus (now called "the empire of Thessalonica") suffered a disastrous defeat at the hands of the Bulgarians at the battle of Kilokotnitsa.
This event caused the Empire of Thessalonica to disintegrate, and so the Empire of Nicaea crossed into Europe around 1235 and captured some territory. This was the beginning of a train of events that would eventually lead to ruin. But it was not clear at the time. By 1248, the empire of Nicaea had captured the whole area (Thessalonica, Macedonia and Thrace).
In 1242, the Mongols defeated the Seljuks in Anatolia. But instead of taking advantage to recapture lost lands, Nicaea spent the years up to 1261 fighting Epirus and the Latins in the West. This proved to be a historic mistake.
After 1261, the relentless focus on wars in the West left Anatolia stripped of defenders, taxed heavily, and open to Turkish ghazis fleeing the Mongols. The usurpation of the throne by Michael VIII, and the blinding of the true Laskarid emperor, left many in Anatolia deeply unhappy. Michael's union with the Catholic church meant the prisons were soon full of Orthodox clergy and their supporters. The people felt their emperor had turned his back on god. Divisions within the church sapped unity from within, while Michael's expensive wars and diplomacy bankrupted the empire. Rebuilding Constantinople further stretched resources, while Anatolia was neglected.
Michael's policy did not work in the end as the West still attacked Byzantium relentlessly despite the unpopular submission to Rome. It simply further weakened Byzantium from within and turned the people against the state.
After 1282, Andronikos II came to the throne. He attempted to repair the damage by making drastic cuts to the military, abolishing the army and the navy, cutting taxes and attempting to live within the empire's means. But this policy proved to be a disaster, as it left the empire utterly powerless and defenceless as the Turks conquered Anatolia and the Italian states fought wars and raided the Aegean at will, sacking and burning Byzantine lands and looting at will.
By 1338, Byzantine Anatolio no longer existed. In its place, Turkish beyliks ruled the territory, and many former Byzantine subjects had already converted to Islam. They could see which way the wind was blowing, and they made the understandable choice that it is better to be on the winning side.
In my opinion, a more successful empire of Nicaea would require a different outcome at the battle of Klokonitsa in 1230. Say the empire of Thessalonica wins a resounding victory over the Bulgarians instead of being defeated. They capture Constantinople shortly after.
In this situation, there is no opportunity in Europe for Nicaea to expand. If a peace can be maintained between the two successor states, then when the Mongols defeat the Seljuks in 1242, Nicaea will march east instead of west. They desperately need to do this. If they can recover and fortify areas like Eskisehir, Philadelphia, Attaleia, and maybe Sinope, they can begin to push into central Anatolia. This would give them the chance to build a real power base.
A general like Alexios Philanthropenos, who gained local popularity and support from Greeks and Turks alike, with Turks even joining his army alongside Greeks, would be ideal. (Historically he lived around 1295 and was blinded for his efforts). A leader like that could unite the locals and the Turks under one banner, potentially changing the course of history.
Best case scenario, he is even able to capture Konya (the Seljuks capital), perhaps on the basis that Nicaean rule is seen as preferable to being conquered by the Mongols. At the result, we now end up with a large and powerful kingdom based at Nicaea, which rules most of Anatolia. Such a state, if it can hold together, would then raise the intriguing possibility of an Anatolian kingdom eventually conquering Constantinople. And when it does, it would be a Greeko-Turkic Anatolian Christian state called Nicaea. That would put Byzantine civilisation back on the map, potentially lasting down to the present day.