The BPPE was formed because California was the world capital of diploma-mills in the 80's. It falls under consumer protection, similar to how California has a special bureau that punishes scummy "extended warranty" companies.
The reason you register is so the state can periodically check your marketing material and field students complaints. For example, Lambda School lied about how many students get jobs, and it would have been real nice for the agency to have stepped in before the lawsuits, which are still in litigation.
It's not about the importance of the act of filing paperwork, it's the fraud of lying to customers that you are following the law and then taking their money. For what it's worth, I don't think prison would help. But maybe some non-dischargable liabilities and a ban from being a corporate officer would.
If you were actually to commit fraud regulators can come for you whether you register or not. The act of registration is simply to make it easier to tell regulators what is happening.
The “California Bureau for Private Postsecondary Education”? This is indistinguishable from parody.