I think a major fear (voiced or not) is that making the process seem any more complicated will scare off J. Random Wiki Editor from citing any sources at all. I'm not sure how real this fear is.
It is definitely the case that we'd rather a bad cite than no cite. Because at least, then, one can check the source out. This is why language of calling sources "acceptable" is possibly counterproductive; it's not the CITE that's unacceptable, it's rather that some sources are insufficiently accurate.
There's a distinction between "acceptable to mention" and "acceptable as verification". Even if one's source is not that solid, and thus doesn't count as verification, it certainly should still be mentioned. Most articles are works in progress and thus will have gaps in verifiability. Mentioning one's current best source (even if a possibly unreliable source) is still a good thing to do.
For example, I will use a random web site for a source, but I will know that that source is only an "interim" one until I can find a better one.
-Matt (User:Morven)