The major credit reporting agencies have the ability to prevent consumer credit reports from being requested without permission by "freezing" a consumer's account. When this is done, a consumer must explicitly "unfreeze" his/her account to allow a credit check.
A frozen account reduces the risk of ID theft to almost (if not completely to) zero because a thief attempting to borrow money, get credit or get a mortgage or buy a car, etc using someone else's identity would be unable to produce a legitimate credit report. This is far superior to "monitoring" accounts.
I propose that when there is a data breach, whether commercial or government data is stolen, at the least, the credit reports for all those people affected would be immediately frozen.
Ideally, this should be done proactively.