Ad fons, back to the source. What does the Covenant actually say? Here is a bit which makes me wonder whether some are fussing over nothing.
"4.1 Adoption of the Covenant
(4.1.1) Each Church adopting this Covenant affirms that it enters into the Covenant as a commitment to relationship in submission to God. Each Church freely offers this commitment to other Churches in order to live more fully into the ecclesial communion and interdependence which is foundational to the Churches of the Anglican Communion. The Anglican Communion is a fellowship, within the One, Holy, Catholic and Apostolic Church, of national or regional Churches, in which each recognises in the others the bonds of a common loyalty to Christ expressed through a common faith and order, a shared inheritance in worship, life and mission, and a readiness to live in an interdependent life.Fussing Over Nothing?
(4.1.2) In adopting the Covenant for itself, each Church recognises in the preceding sections a statement of faith, mission and interdependence of life which is consistent with its own life and with the doctrine and practice of the Christian faith as it has received them. It recognises these elements as foundational for the life of the Anglican Communion and therefore for the relationships among the covenanting Churches.
(4.1.3) Such mutual commitment does not represent submission to any external ecclesiastical jurisdiction. Nothing in this Covenant of itself shall be deemed to alter any provision of the Constitution and Canons of any Church of the Communion, or to limit its autonomy of governance. The Covenant does not grant to any one Church or any agency of the Communion control or direction over any Church of the Anglican Communion."
For some the fuss seems to be, If we sign the Covenant we will hand over our autonomy, we will be submitting decisions made (say) by a disciplinary tribunal in our church to the higher power of the Communion's Standing Committee ... that is scary, and at all costs to be fought against. I cannot square that fear with 4.1.3. Can you?
For those who love the Lord Jesus Christ and love his church, what is in the Covenant which is fearful?
Take 4.1.1. What is objectionable here to a Christian who reads Scripture obediently as it presents Christ praying for the unity of the church, Paul expounding the unity of the body with its diverse members, the writer to the Hebrews urging readers to meet together, and various writers urging Christians to love one another? Is it not intrinsic to being 'in Christ' that we wish to grow more deeply into that state, both by becoming ever more loyal to Christ, and ever more deeply bound to those who are in Christ with us, our brothers and sisters in God's family?
Is it possible that Anglicans as a group of Christians have a particular deficit of knowledge of the theology embedded in 4.1.1? Has, for example, the concept of a 'national church' and of 'autonomy' limited our frame of reference and our horizons in respect of the possibility of commitment to the aim 'to live more fully into the ecclesial communion and interdependence'?
When we love the Lord Jesus Christ we love everything about him: what he teaches, who follows him alongside us, what he is making of those who love him, ut unim sint. Nothing in the citation above from the Covenant is inconsistent with this love.
Perfect love casts out all fear. For those who love the Lord Jesus and love his church, there is nothing to fear in the Covenant.