One way to appreciate what a huge difference the Covenant would make is to ask what difference it would have made if we already had it.
Over the centuries there have been many changes. Some have been changes of ethical judgement. Christianity no longer approves of slavery though it did for most of its history. It permits lending money at interest, which it forbade for most of its history. In the twentieth century the Church of England permitted contraception and divorce, both of which it had previously condemned, and supported the abolition of capital punishment. The current focus on gay and lesbian sexuality is one of many; in the light of history we can be sure that the concerns of Anglicans will move on to something else in the course of time.
In practice ethical attitudes change, and the Church's moral teaching changes too - often more slowly and carefully, but change it does. The process of change is always untidy. Whatever the resolutions of committees and the pronouncements of archbishops, the real driving force is changing attitudes in society at large. Personal experiences, stories of other people's personal experiences and reflection on how those experiences relate to one's inherited moral concepts all mix together to generate new considerations. Church authorities cannot control that process. To be open to God's guidance they need to be critical contributors to it: contributors because they bring the insights of the Christian tradition, critical because their conclusions are not predetermined in advance.
Similarly there have been many changes of doctrine. We no longer interpret the Bible allegorically, as the medievals did, or believe we are surrounded by spiritual beings influencing the world around us. If we did modern science would have been impossible. Anglicans today who affirm the Nicene Creed and the Thirty-Nine Articles often interpret them in ways very different from what the texts were originally intended to convey. Such changes are inevitable. Society moves on, errors are acknowledged and new insights are accepted.
There have also been many ecclesiastical changes. Churches change, for example, their orders of service, their regulations for ordaining priests, and the oaths priests are required to take at ordination. Recently many Anglican provinces have permitted women priests and bishops.
In all these cases - ethical, doctrinal and ecclesiastical - if the Covenant had been in force at the time the change was first proposed, it would have given real power to objectors to prevent the change. To do this, they would have needed to do two things, both of which would have been quite easy. Firstly, they would have needed to persuade an Anglican province to submit a formal objection to the Standing Committee. As each province determines its own decision-making system the means to do this varies, but in some cases it would simply be a matter of persuading the archbishop.
Secondly, the objecting province would need to persuade the Standing Committee that they cannot in all conscience remain in communion with a province which makes the change in question. In theory the Standing Committee might have rejected the objection and permitted the change; but the whole purpose of the Covenant is to provide a method for enforcing objections of this sort. Before any Anglican province had declared slavery immoral, the supporters of slavery had on their side not only the entire history of Christianity but also a huge range of biblical texts. The same would have applied in the case of capital punishment and lending money at interest.