First point to clarify: its not actually a secondary 'fermenter'. fermentation should completely finish in primary (when making beer), so our secondary vessel is a clearing tank, sometimes called a 'bright tank'.
Some aging occurs in secondary (really as soon as fermentation completely ends, the aging/mellowing begins). racking to secondary gets you off the sediment and helps promote having a clear beer.
its easy to get sediment racked to the bottling bucket from primary...secondary has so little sediment its easy to avoid.
That said, plenty of people here just go for a longer primary time, like three weeks from pitching yeast, to racking to the bottling bucket. I myself prefer using a secondary.
Wheat beer does not have to look like a dirty urine sample. A hefewiezen should be cloudy...but many American wheat beers are crystal clear. So it depends on the style.
I made a great tasting wit, but because I decided to give it a 5 day secondary, it ended up a little too clear for the style. Luckily I don't enter competitions...I just drink. My stomach doesn't know the difference between hazy beer and clear beer