Just a high level idea but...
Would it be possible to create a distributed system of wallets such that the wallet is created, simultaneously encrypted and then distributed on a system of servers similar to the way Bitcoin now works where an encrypted file is kept on various servers all over the world. And to connect to your wallet you merely need to connect to one of these servers, deposit some money and create a password and from then on that account is your own. Those that run the server could get a fixed interest amount for hosting your account in a similar fashion as the way miners are paid.
Then during a transaction you could just connect to the account network and authorize the transaction.
I have no idea but just figured I would throw that out there.
I've suggested the same thing in the past, and we came to the conclusion that yes, it would be possible, but nothing like it exists yet, so it would be difficult, time-consuming, and potentially expensive to execute.