One of the problems with General Convention is that it is a political body. It makes decisions using political means. This is not a bad model for issues of church order, such as welcoming new dioceses, setting budget priorities, setting up the guidelines by which deacons, priests, and bishops are ordained or disciplined.
But it is a very bad model for deciding theological issues. The problem with the political model is that it is subject to political activism. People now make theological decisions based on political means. The problem with that is the decision is determined before the community does the discernment. And, when discernment is called for, it is called for in a political setting, so those who are politically active or politically driven are the ones who make the statements to the "discernment" committee/group. So, the method of discernment itself is subjected to political activism.
The largest problem with GC is that it uses the wrong means to do theological discernment. It asks, not what is the will of God, but what is the will of the deputies and bishops. All too often, they end up with the will of men and women, not the will of God.
So, how do we discern the will of God? First, we ask God to show us His will. We compare our answers to see if they are congruent with how God's will has been determined in times past (Scripture and Tradition). Looking at Scripture, I am struck by the pain and damage done to God's people when they insist on their own will instead of God's will. Perhaps the greatest example of this is the establishment of a King for Israel. When Israel insisted on a King, instead of letting YHWH be King, they selected Saul and, as a direct result of Israel becoming like the nations, you had the oppression of the poor, the rise of syncretism and idolatry, the dividing of the Kingdom and the people forgetting their covenant with God - and, eventually, the destruction of the 10 tribes and the Exile of Judah.
Looking at TEC today, I see a rise in TEC becoming like "the nation" or like the secular world. We speak of "rights" but not of "righteousness." We have forgotten our Covenant - or at least the first three promises (to continue in the Apostles' teaching and fellowship, to persevere in resisting evil, and to love your neighbor as yourself). We have divided the kingdom and are facing our own exile.