With some logical thinking there are various reasons as to why people are looking to do so.

-- people want to have funds available on exchange to strike when the price falls down hard.
-- people have various sources of income that they want to *temporarily* store on exchanges without disclosing their own identity to the sender of the funds.
-- people look to launder illegally obtained money by using exchanges to buy Bitcoin or whatever altcoins to withdraw that later on (not saying OP has these intentions).

Other than that it has no real benefit, and is even dangerous as some people have also stated, especially so because an exchange at any time could force you to still verify yourself. If you for whatever reason can't prove that the deposits are not 'earnings' from illegal activities, you can basically kiss your money goodbye. It's like you are playing Russian roulette with your money, which is just stupid in times where exchanges have far stricter regulations to abide by than ever before. Purely based on that, I don't even know if it's possible to withdraw fiat without verification....