The Byzantines (I prefer to call them the ERE, but I'll call them the Byzantines as it's more recognized in lay discourse) had been under threat for a long time, and if the Turks hadn't sacked Istanbul/Constantinople, some other polity would have. Western Europeans sacked Istanbul/Constantinople in 1204 and ruled it as part of the Latin Empire until 1261, when it was retaken. The Byzantines ran into trouble with the Bulgarian kingdoms and the Kievan Rus constantly, along with their Islamic neighbors. If it wasn't the Turks it would have probably been the Bulgars or the Rus.
