Personally I am a bit nervous about commune models because of some of the big cult disasters that came out of the 60s. This model can be a bit naive about human nature. I can think of more than one notorious example of one-time orthodox churches that went seriously off the rails with charismatic leaders (not in the theological sense) who got too full of themselves.. one factor was that the ‘pooling’ of members property/income ended up being abused by the leadership. There are major issues of accountability and transparency around this issue.
How do TCH navigate such issues?
I have been thinking a lot about this about this aspect of expressing genuine one anotherness in community.
first, i dont think commune is the right word. if church reflects the nature of who God is it would be fair to say Trinitarian or persons in community - but not commune in the socialist sense. People have thier own lives and stuff but they give themsleves to sa deeper sense of connection or ownership in community. Church is more a family dentity than an organisation centred on a sunday event. church in that sense does what families do (or should do).
second , we need to remember that individualism has a massive sway in the way we think about spirituality. And this is often evident in our churches. TCH model is in part addressing this by enmphasiing the very biblical apsect mutual discipleship - and in doing so it rubs up against our indiviualism, not biblical ideals.
third it not about common ownership of goods at all. Individual members are free to use their stuff how they see fit, but part of letting the gospel centre our lives is using our stuff in service of others, including our homes,cars, money etc. Its is an attempt to tangibly express the different parts of the body looking after each other.
fourth, becasue of a geuninely plural leadership structure and a high emphasis on mutial encouragement and exhortation, it makes it harder for an abusive power relationship to occur. The usual Anglican rector power relationships are potentially far more abusive becasue he exercises leadership in a hierarchial structure as opposed to a plural elder structure.
finally
there is a sharp emphasis on the gospel word ruling and controlling life together. again the sense of mutual discipleship , encouragement, exhortation and discipline means that everyone is encouraged to be leading in some sense through service of the other. Whilst there is still a place for eldership, I reckon the high level of owning ministry guards against the kind of potential abuses you are imagining