I don't mean dodging regulations. It's possible to keep all standard regulations on the blockchain but without all the paper work using smart contracts.
That way you avoid all the corrupt middle-men like the lawyers and government clerks.
Why do you need it public? So it can be audited.
Why do you need it distributed? So a copy can be obtained and kept on every computer giving it credibility and robustness.
Why do you need decentralisation? To avoid corruption. The little computers doing PoW are securing the network from corrupt humans.
Why is it efficient? Because having offices in downtown, employing tens of thousands of humans that audit, test, check, read, sign documents is not efficient and makes no sense when computers can do it better, faster and a lot more secure.

It's not a strawman example, read about colored coins, they allow listing any asset right on the Bitcoin blockchain. It's possible, problem is that it has no meaning nowadays but if governments decide to list assets on the blockchain than turning all that paper records (or sql databases) to a public record listed right there on the bitcoin blockchain and secured by PoW is easy and each owner will have a private key or a P2SH address proving his ownership with no doubt.

Suggested reading:
http://unenumerated.blogspot.co.il/2017/02/money-blockchains-and-social-scalability.html