I already started to do that. I have build so called "brigdes to pass" wallets which are not connected to each other so no one from the sniffers can know how much bitcoin I have in total, where do funds come from and where do they go. Isn't Bitcoin all about privacy and safety in the first place or do I got it wrong since the beginning a few years ago ? I do this because lately in Italy there has been quite some arrests for frauds in Bitcoin and that is one of the reason SKRILL restricted my account in the first place, (am still waiting from their side to lift my restrictions). I don't want to be on such radars cause I have no reason to be there, simple miner which keep my mining activity in a nearby country to pay less than half price for electricity.
If you don't want them to track you, consider using a mixing service (Check my sig), it does its job well in that field. They might not be connected with each other but transactions on each address is viewable to everyone and it could still be usable in tracking, especially if there's an address connected to an exchange.
Going back to your question, I too haven't heard of any exchange which allows you to do that, but I remember asking my local exchange the same thing and they said no.
What I think is, your unique address is somehow your name that indicates "it has something to do with you". Exchanges have this AML/KYC policies so having a unique address would be easier for tracking and making sure the user is adhering those, i guess.