How about looking at it this way:
Let's say, you have a precious rose plant. You wouldn't put it by the roadside, would you? By the roadside, your precious rose plant would be dirtied by the dust of the passing cars. And there's always a chance that some irresponsible person might just pluck it. Or a passing cow might eat it. Or worse yet, a dog might piss on it.
So, you would keep your precious rose inside a walled garden, wouldn't you? So that only the right persons can appreciate its beauty.
Women, in Islam, are definitely more precious than any rose plant. They are our mothers, aunts and sisters. They are the bearers and nurturers of the next generation of Muslims. They are given a task which no men, however strong or clever, can handle. After all, despite the advances of science and technology, it is still women who bear children and suckle them, not men.
So it is the duty of the men to protect the women. Clothing that covers the aurat is just part of the hijab which is used to protect the women.
What a woman wears under the veil is not something I can see. However, it would be kind of weird for a practicing Muslim woman to wear, say, a thong under her veil. It just doesn't feel right but that my personal biased opinion.
WaLLahu aklam.