Lacking direct evidence, I think the reason that some ministers have a vote at General Assembly is because the Unitarians and Universalists consolidated. Those who criticize the practice seem to think the Unitarians merged with the Unitarians.
Not to pick on the UU Enforcer, but he broached the subject and better to get this off my chest now rather than wait until someone says something silly about it later.
First, here's the UUA bylaw in question. (Unblockquoted as it was ruining my valid XHTML. Dunno why.)
(b) Minister Delegates and Religious Education Director
Delegates. Each certified member congregation is also entitled to be represented at each General Assembly by the ordained minister or ministers in full or associate ministerial fellowship with the Association settled in such congregation, and by any minister emeritus or minister emerita of such congregation in ministerial fellowship with the Association designated as such by a vote at a meeting of the member congregation not less than six months prior to the General Assembly, provided that such minister has been settled previously in such congregation, and by the director of religious education who is accredited by the Association and employed in such congregation.
Why ministers, and now DREs? Because, like the congregations, ministers have a fellowship-relationship with the UUA. Voting is a right based on the relationship. I think Universalist ministers would have had a right to vote at state convention by the right of the membership in the Convention whether or not they were actively serving a parish. The alteration in the polity of the UUA undid that relationship, but I gather the minister emeritus relationship is something of an analogue. That ministers are delegated from a congregation realigns the membership from the State Convention to the local congregation. Since that's no difference for the Unitarians, the other alterations must seem like a novelty to them, rather than an adaptation of Universalist polity.
I'm still not happy about the DRE voting provision because the relationship between uncalled persons and a church is different than one who is called. I suppose I could make a theological case, but that's not likely to convince many people. Pragmatically, the relationship is harder to intitate and end. But at least it is based on the same dynamic of UUA vetting and congregational (for lack of a better term) mutuality.