It would be interesting to extend personal information with discardable identifiers, similar to throw-away email aliases.
If one is compromised, you delete it, but the main ID is protected.
A similar concept can be developed for SIN, adresses, and other information.
Key personal information could be checked by a central authority if that is actually needed.
ID theft would be greatly mitigated when you can log in to your citizen portal, and check an alias to your SIN as compromised.
You can even take it one step further and leverage public key cryptography, where you're issued digital keys with revocation dates, and a digital fingerprint.
If you get a notification it is in a breach, it takes one command to remove its value. The central authority could do it in one fell swoop for 1000+ citizens.
The central authority would need protection, but at least you reduce the surface from anyone that ever hovers up your data to one party, with a local MP on hand for some oversight.
Enforcement and education will not do much as long as the business model has such high returns.
It is possible to reduce the market/demand in some of these scenarios, but few economies seem to dislike companies that harvest data, so I'm not holding my breath.