I would guess that the idea came about as it does with much of teh rest of contract law - Are the parties to the contract able to understand it and consent to be bound by it?
If someone is significantly mentally disabled then there are, IMO, very good reasons to question their ability to comprehend and consent to marriage. There is also a good possibility that they may be taken advantge of.
I noticed this at the end of the linked article: "I suggest amending the guardianship laws, both EPIC and the Mental Health Code, to permit a sensible evaluation of marriage by the probate judge. Does the person
with a disability want to get married? Does the other party have a history of violence? Does marriage pose any health or safety risk for the disabled person?"
There is nothing in his proposal that recommends that the judge determine if the disabled person is competent enough to understand what marriage is. I would think that would be one of the first things for a judge to determine.
I don't know what the laws are in other states. I do know it is possible in at least some - there have been several mentally disabled couples on various TV talk show programs over the years. From reading this: http://www.cqcapd.state.ny.us/counsels_corner/cc28.htm
it appears that the mentally disabled may marry in NY State for example.