Demetrios said:
Well, it's unlikely that there would be a 1204 scenario after an 1187 one was annouced. They are only 17 years apart, after all...
On top of that, the first 2 times the idea was seriously adopted to make a Crusade out of seizing Constantinople were:
1. When Emperor Frederick I was passing through on the 3rd Crusade (1189), the Byzantine Emperor threw his ambassadors into prison and broke the agreements they had concerning supply, transport, etc.. So Frederick scattered the Byzantine army escorting him and seized Adrianople and Philippopolis. Wintering in Adrianople, he wrote to his son Henry VI to meet him in Spring with a combined Pisan-Genoese-Venetian fleet before the walls of Constantinople. With his huge German army attacking from landward, and the "imperial fleet" from the sea, he planned to capture Constantinople and 1) remove it as a traditional obstacle for Western armies passing through; 2) use it as a forward base to recapture Outremer; and probably also 3) to reunite the 2 Empires under himself. The Byzantine Emperor then realized he'd overplayed his hand, released the Germans, and agreed to supply their army and ferry it across to Asia.
2. When Alexius III deposed his brother Isaac II (1195), Emperor Henry VI, already gathering a German army and Italian fleet, prepared to conquer Constantinople and install his brother Philip I as Emperor in right of his wife, Irene (Isaac II's daughter). The Lords of Cyprus & Cilicia-Armenia agreed to hold their lands as imperial fiefs, and in return were each crowned King by the German Chancellor despite the protests of the Byzantine Emperor. Before the army sailed, Alexius III bought his way out with a large sum of money and an agreement to pay annual tribute. Henry's army then bypassed Byzantium and sailed for Acre on the "German Crusade" (1197).
So the idea was floating around in Germany & Italy starting with the 3rd Crusade, and even before if we count the Normans' attempt to capitalize on the 2nd Crusade by invading Greece (1147).
It can even be argued that #2 above set the ball rolling for the 4th Crusade, as it was Isaac II's son, supported by his brother-in-law, King Philip I of Germany, that diverted the 4th Crusade to Constantinople.