Well, I don't know of any of the seven that were not called in response to the ferment of the Church over theological matters.
But quite a few of them were really just local councils, whose decrees were not accepted by all at the time of their passing, and often required years or even decades to be received by all Churches. None of the Great Councils called themselves "Ecumenical Councils", nor did they view themselves as having any kind of "infallible" charism. That was ascribed to them later, after their teachings were received as part of the Tradition. Conversely, there were councils that bore all the earmarks of being "ecumenical" but which were rejected. The "Robber's Synod" of 449 very self-consciously pronounced itself to be "ecumenical" and binding, but its teachings were rejected.
We also have to look at some later councils. On Bellarmine's list, the Synod of 869-870 is listed as the "Eighth Ecumenical Council", but its decrees were not only rejected, but burned in a copper bowl at the Synod of 879-880. That synod was ratified by Pope John VIII, and its decrees accepted as binding, for more than two centuries. It was well on its way to being considered as ecumenical (and many theologians today think that it provides a useful basis for any future reconciliation), but the Latin Church rejected it in the eleventh century, effectively flushing it down the memory hole. So why is the Synod of 869-870 "ecumenical", while the Synod of 879-880 is not?
We could also look at how the Latin Church dealt with its own general synods, in particular Constance, Basle and Florence-Ferrara, to see that "ecumenicity", even within a Western context, is not automatically ascribed, but requires a process of reception, and that councils apparently received can be disavowed in whole or in part. As Ravenna says, reception determines ecumenical status.
