I see. well there is a couple of issues here. in exchanges there are large liquidity providers who specialize in trading. so you're not just send a couple of BTC for $, but potentially dealing in large volumes of trade. you're just not allowed to do that without following AML/KYC. sure, if you doing small volumes likely nobody is going to notice, but for the system to work on large scale you need big processors (market makers).
also what is missing here is the element of price discovery. That is what exchanges are all about. The bitcoin exchanges gather order data, take the fiat money and settle the trades. so if you want to settle 1'000'000 tx/sec, you can't have a completely inefficient system. I very much doubt that one can work around the existing clearing banking system, to settle fiat transactions.
OK, so again it comes down to which problem you're trying to solve - (1) or (2) as I referred to in my first post. I think like many earlier discussions, you are mixing them. That's OK if you want to solve both of them simultaneously but I think it helps to separate them. As for scale and AML/KYC, for sure that's a problem; but one of the main points about decentralisation is that it reduces scale. No centralization means no large scale transactions (or at least, no transfers larger than is usual for that particular entity).
I think we can all agree that clearing is an issue in the fiat world, but not an issue in the crypto world - there, settlement occurs atomically with the transaction because of irreversibility, so there is no clearing.
Performing clearing and settlement for a decentralised fiat-crypto exchange is indeed going to be tricky. Centralised - no problem, it's just like any other currently existing trading system. You can imagine things like T+2, netting etc. existing in that framework if the system gets complicated enough (e.g. brokers) but it's all bound to be much cheaper than the existing system because it's so easy to get to a final settlement when you want.
For decentralised, I could imagine it having two tiers. For high transaction throughput crypto-crypto asset exchange, you'd need some kind of settlement into crypto (for the transition from sub-second trading up to minutes/hours bitcoin settlement), and then a second layer of settlement of bitcoin-fiat using traditional bank clearing, on the order of days. This is what we currently have really at the big bitcoin exchanges; they do it poorly I guess but they do it. Trying to make all that work in a decentralised manner is seriously difficult. What I was describing in my earlier posts was a system to help with the on-ramp part - how to do settlement of fiat/crypto without a central server.
However I have envisaged a system like this: a p2p network of users who hold fiat accounts and bitcoin accounts. Fiat deposits and balances are tracked using ssl logging (so verifiable by the whole network), and these provide the liquidity to allow real time trading peer to peer of fiat for bitcoin. Imagine the network as a whole as an entity having a USD balance. Peers add $1000 when they enter and are credited with that amount in the globally maintained ledger (blockchain comes in handy!) - the mechanism to "add $1000" to the ledger is to make a deposit to one of a class of users who act as depositories, and who have pledged an equivalent, or usually much larger, btc amount to multisig (so they can't run away with it and liquidity is maintained even with price fluctuations). So, these users hold dollars on the network's behalf. Then fiat-btc trading can occur within the network in real time and when time comes to settle out into fiat, any of the depositories can make the wire transfer.
Obviously that is an enormously complex structure to build, but with the ability to verify fiat balances cryptographically, it *is* possible.
As for high transaction throughput and price discovery, I don't have a strong opinion. For sure that is the natural preserve of a centralized system, but perhaps with imagination you can make price discovery work in a decentralised way. Not sure.