All the concern about this dye is based on a 1990 study where they fed rats 0.5%, 1%, or 4% of their diet by mass with the dye. Only the group with 4% of their diet had an effect on thyroid stimulating hormone, and follow on effects on t3 and t4. This increased stimulation of the thyroid is what they hypothesized is responsible for potential tumor growth. That dose is ~5,000-15,000 times higher than a regular diet. Increasing sugar or alcohol or literally anything else in your diet by that amount will have dire consequences.

Furthermore, the authors mention that a 100x dose human trial had increased TSH, but without changes to t3 or t4. This (and other factors they bring up in the paper) show that humans don’t respond like rats, so these rat studies can’t really be applied to humans. Even a massive overdose wouldn’t have the same potential for causing cancer in human as it does in rats.

All that said, there’s no benefits to the consumer to have food that’s just more red. Banning red 3 isn’t going to make manufacturers stop dyeing food red, it’s going to make them switch dyes, which might not be able net positive.

The FDA’s notice even says this:

two studies that showed cancer in laboratory male rats exposed to high levels of FD&C Red No. 3 due to a rat specific hormonal mechanism. The way that FD&C Red No. 3 causes cancer in male rats does not occur in humans. Relevant exposure levels to FD&C Red No. 3 for humans are typically much lower than those that cause the effects shown in male rats. Studies in other animals and in humans did not show these effects; claims that the use of FD&C Red No. 3 in food and in ingested drugs puts people at risk are not supported by the available scientific information.

They mention that they are forced to ban it due to a technicality of the law:

The Delaney Clause, enacted in 1960 as part of the Color Additives Amendment to the FD&C Act, prohibits FDA authorization of a food additive or color additive if it has been found to induce cancer in humans or animals.

So even if we know for sure that a substance is fine for humans, if there’s any animal that could be given cancer by ingestion of any dose, it legally should be banned.

For example, if you did a study where you fed dogs chocolate for a year, and they developed liver cancer due to the constant poisoning, you could petition to have chocolate banned as a food edditive.