Sounds pretty similar to the English system to me :
"We threw out the British system. In our system, all titles are on a register."
So are the vast majority in England. There is some unregistered land still, but it gets registered when a transaction is made. Over time all land will become registered.
"Once the contract is unconditional, you're buying and selling."
Same as in England. People can pull out after exchange of contracts, but the contract normally stipulates a massive penalty. How much can vary with the contract as per the wishes of the buyer/seller.
"The contact may well be unconditional from the start and the deposit is paid up front. If the buyer doesn't settle the seller keeps the deposit."
Can happen in England if both the buyer and seller are willing to have it.
"The more conditional the offer the less likely it is to be entertained."
Sellers in England have exactly the same choice - who they choose to sell their house to and on what terms/basis. Buyers have a choice whether or not they want to buy on those terms.
"We offered unconditionally on our current house within a week of seeing it which meant getting the house inspected, the title checked and finance arranged. Chains are not common. There is no failing to settle except in extremely unlikely and rare circumstances."
I think this is the difference in England, that this process can take some time. However it doesn't have to, you can make it take a shorter amount of time, and demand a buyer does it in that time as a seller. It adds to the cost of course, and reduces the number of potential buyers who will proceed on that basis.
"There is no failing to settle except in extremely unlikely and rare circumstances."
Same as in England. Once contracts are signed it is very rare for the process not to go through to completion, as the financial penalty is large.