The Byzantine Empire did not fall due to the crusades but because it had become politically ossified, culturally and religiously confused, and militarily unsustainable. The Byzantine leaders could not judge what the rise of the Ottoman Empire meant for their nation. They thought that they could negotiate and even collaborate with the Ottomans. By the time they realized that negotiations wouldn’t work against the Ottomans, who were determined to conquer everything that the Byzantines had, it was too late.
The crusaders cannot be held responsible for the rise of the Ottoman Empire either—that was caused by factors related to the ambition and vision of the Ottoman emperors, their ability to take advantage of the opportunities for expansion in the oriental lands and southeastern Europe, their military might, and the geographical and political situation during the Middle Ages.
There is a gap of 250 years between the crusader sack of Constantinople in 1204 and the Ottoman conquest of the Byzantine Empire in 1453—it is hard to draw a connection between the two events. The Latin Empire which followed the 1204 sack of Constantinople lasted for two generations. During this period, the leaders of the Byzantine Empire retreated into smaller states, one of them was the Empire of Nicaea, which reconquered Constantinople in 1261 and proclaimed that the Byzantine Empire had been resurrected.
The irony is that the resurrection of the Byzantine Empire made it an even better target for the Ottomans, who were as much interested in the legacy of the Byzantines as they were in territory and wealth. The Byzantines ignored the fact that empires always prove easy to proclaim but are hard to govern and defend.
If the Byzantines had visionary politicians, culture leaders, and military commanders, they could have secured their Empire after 1261. But they squandered their time and energy in negotiating with implacable enemies and seeking help from Western Europeans who were themselves powerless against the political ambition and military might of the Ottoman Empire.