1. I can totally see the "Covenant Initiated by God" concept working in Biblical times when God was pretty vocal about what God wanted. But if we're to have covenants these days, then how are we to know that God is initiating them if God is silent on the matter?
2. Also, how do we have a binding agreement between parties without the consent of one of the parties (i.e. God)
3. Assuming PB's idea that one cannot have a covenant per se without reference to God catches on, and it might well do that as she is a well-respected and convincing person, then I assume that covenants will not be used in UU churches much as most UU churches have at least some atheists and for the church to think of itself as "A people covenanted with God...and those guys" probably wouldn't work. As the word "covenant" has been used for secular agreements for a long time, I don't see why we can't stick with that, but if we can't it would be nice to come up with another term for the process of a church coming together to talk about who they want to be as a community and to make agreements with one another because the process still strikes me as a sacred one even without God's direct involvement. The best I can do for a name for that is "Pact," yet I find that "Pact" has Faustian* overtones.
4. As an aside, if we use "covenant" the way it is used in property law, PB's definition can still more or less work. Covenants in property law are rules that govern the use of the land set by a seller** or giver of the land, so I suppose one could say that God is giving the church to the people provided they obey God's rules. But it is unusual for those rules to be discussed and put together by the recipients of the land without direct input from the original owner.
* Fausto-ian overtones I could live with. I think.=
**For a simple example, you can sell your land to someone with a condition that they will never cut down your favorite tree or move the grave of your dog Fluffy. If they violate the covenant, then you can sue them. The most evil and the most famous kinds of restrictive covenants are the kinds that don't allow houses to be purchased by black people, but those covenants have been found unconstitutional by the SCOTUS (Shelley v. Kraemer) and thus unenforceable.