I wouldn't call legal force to be deputizing anybody. If those entities don't do as the law says they will be in trouble themselves. Deputies have authority. Banks and stores are just following the rules and report to authority when required.

You're picking a pretty fine semantic distinction, and IMO if you're going to be a pedant, you should try to be correct. Deputization isn't my invented description for this model; it's more broadly used. E.g., https://www.bitsaboutmoney.com/archive/money-laundering-and-...