Nah, then it becomes a popularity contest instead of picking someone who would actually do the job properly and treat it with respect.
In some ways, it isn't a bad idea, as people are more likely to look up to a Mod they chose. In otherways, it is bad, because a nominated Mod will get away with breaking minor rules and a spot of bad behaviour because they are so popular, when they should be following the rules to a letter. Plus a nominated Mod could always be lazy and not carry out their duties completely, using the excuse that they didn't ask for the job to justify it.
Also, chances are those who get nominated would not wanted to be a mod, simply because they have more fun with the freedom to break rules and not having to set an example than they would have by being a mod (I'm looking at you Tom...)