This seems like a good idea, in principle, if the biosecurity officers could have any real power to do inspections, evaluate safety, and enforce compliance.

In my opinion, the only real way to get universities to take biosecurity risks seriously is to make them legally liable for damages if there's a harmful leak -- and to force them to take out insurance policies to cover the expected costs of such damages. In other words, use the legal system to force universities to 'internalize' the likely 'externalities' they're imposing on the rest of the world.  This would require coordination between university ethics committees, biosafety inspectors, University Counsel/legal officers, insurance companies, and upper administration.

Of course, this might make certain kinds of biological research prohibitively costly -- but if the expected value is negative (given the biosecurity risks), then it should be prohibitively costly.