How would you design the ultimate exchange?

I think the ideal exchange is not a single exchange, but a network of nodes.

It should be easy to transfer FIAT to and from. Guess that would mean that there should be at least one node in every part of the world, as apparently transfering money to and from banks sees to move at some set speed/distance. (A lot easier to move fiat from germany to UK than to Japan.)

The nodes should have their own USD and BTC blockchain, where they have to deposit fiat in a locked account where at least two OTHER nodes have to confirm for founds to actually be transfered.
If a node runs out of USD in their account, it has to temporarily suspend trading. At set intervals, the nodes should exchange USD and BTC depending on what they owe eachother.
The seperate blockchains are just for arbitrading between the nodes, so that all nodes know that the other nodes can cover their trades.

Say user A is in Belgium on node X, and user B is in India on node Y. Since the nodes are constantly updating offers between them, user A can see user B's offer, and sends a buys order for 1 BTC@100$ to node X. Node X checks its own offers before sending a BUY order to node Y. After confirming the deal is sealed. User A now has a BTC in his accont and user B has 100USD in his account. The amounts are also sent to the node-networksblockchains. Later that day, exchange X, Y and other nodes do an exchange of the actual fiat and BTC(or every time a trade/treshold have been reached).