I don't think off-blockchain is the answer. This completely undermines and defeats the purpose of the block chain being an open ledger. You might as well be another Paypal. The reasons invoked for off-block chain transactions are that the merchants’ volume is too high for the block chain, that the fees are too high or that confirmation time is too long. For every single of those problems there are known solutions that aren’t detrimental to the block chain ecosystem.
I think the "another Paypal" solution is exactly what you want here.
The only difference is that this
paypal would also provide anonymity and non-reversibility of transactions.
You could create an account there without providing any personal data, possibly even from behind Tor.
The service doesn't care who you are because it does not need such knowledge. It is there to provide instant payments using the coins you first deposited there.
And this approach could also address the transaction volume size.
Because the service does provide insurance for non-confirmed bitcoins transactions, but bitcoin trasnactions will eventually become expensive so the merchants will have an incentive to get single bills paid not through the chain, but "internally". And only withdraw it like once a day.
Of course a decentralized solution for off-chain transaction would be much better, but it is also a much harder problem to solve, so IMHO centralized solutions that focus on anonymity will come out first as more popular (just like centralized black markets or centralized mining pools have).
There is no reason why a service like Bitcoin Fog couldn't be turned into a payment processor - they already have good privacy protection infrastructure and only need to start supporting internal transfers between accounts.
Of course the governments will not like it and their minions will quickly attack the idea all over, using all kind fo cheap propaganda, but who cares about these dicks anyway.