However that doesn't necessarily imply its banned on the basis of solid science either.
Whether you agree that substances linked to cancer should be banned or not, that is the standard in public health policy, including in the United States. "Solid science," as you call it, does not always inform public policy, nor should it, and that's coming from a scientist. Food recalls would never happen if they were based on "solid" evidence of widespread harm. It's always about the risk of any potential harm. If there is simply a potential, it is often in the public's best interest to remove that risk.
If it were not for the fact potassium bromate was already in use before the 1958 Delaney amendment to the 1938 Federal Food, Drug, and Cosmetic Act, the FDA would have banned it just as other world health agencies have. Any other substance with the exact same nephrotoxic and carcinogenic properties would be prohibited from being introduced into products today.
Can someone make a perfectly safe pizza using bromated flour? Sure. Do they have the analytical equipment necessary to determine they've done just that? I'm going to say most people don't. Just like most people don't have microscopes to determine if the spinach they brought home from the store is free of salmonella, so as to ignore any recall.
It's only fitting that people should choose to self-govern on the same principle found at the root of public health policy. People have a right to feel safe.