Before I start suggesting changes to the UUA, I'd like to talk about the fused Unitarian and Universalist polity pieces we have. Well, mostly Unitarian, meaning it is at heart a service bureau, a meeting of ideas, and a ministerial settlement service. But the Universalist idea of church -- especially postbellum -- was local and non-local alike. This culminated in the redubbing of the Universalist General Convention as the Universalist Church of America. The Universalist church was local, state-wide (through its conventions) and national. Really international, given its conspicuous presence in Japan, and to a lesser degree, England.
A minister was Universalist because he or she had a particular relationship -- sorry to be vague but this relationship changed over the years -- with Universalist professions of faith, and had the fellowship of the state convention (or the General Convention when there was no state convention.) Same with the churches. The church collectively had a particular relationship with Universalist professions of faith and fellowship in the state or General convention. Universalist churches had Universalist ministers. If one decided to shop around for a non-Universalist minister or church (respectively) fellowship could be withdrawn! (Dual fellowship between Unitarian and Universalist ministries was a key step towards consolidation -- and the death of many Universalist churches, who couldn't afford to outbid the clergy-strapped Unitarians.)
Until the first decade of the twentieth century, many or most local "churches" were really two twin entities: the church (of believers, led by the pastor and deacons, and was the holder of the sacraments) and the parish (led by a lay moderator, of attendees and contributors, focused on teaching and public morality), with a great deal of overlap in their memberships. OK: that's drawn pretty broadly, but you get the idea. Those familiar with Unitarian origins will recognize this senario: with few exceptions, the Standing Order parishes in eastern Massachusetts became Unitarian; the churches clothed themselves in new "second" or orthodox parishes and became the Congregationalists.
Some Universalist "churches" were mostly parishes (a.k.a. "societies") and some parishes didn't have a church-twin (as a company of professed believers) at all. Unless I'm mistaken, parishoners didn't have to make a religious profession. Many a Universalist convention sermon scolded lazy parishes for not gathering churches. In time, for the sake of administration, churches and parishes were encouraged to merge, and the parish-nature eased out the church-nature. I have observed that those Universalist churches that retained Christianity were those that preserved independent churches and parishes (very few) or retained distinct churchly features. Also, the sacraments started drying up before Christianity fell from the norm.
OK -- like how does this matter? Well, for one it is important to understand how we got here. It wasn't some post-1946 weirdness in the water, but the succession of the polity, and the Unitarians started there.
But mostly this matters because the interlocking relationships of this polity survive in how we do ministerial fellowship, if in a flattened form. If the UUA were to be radically simplified or changed, this might be the last function to go.
Or we might adopt a Unitarian-Congregational mode of fellowship via councils. Alice Blair Wesley's recent Minns Lectures would suggest a trajectory, but I think it would be rather unpopular.
The last option would be perfect independency. Again, unlikely.