FDA doesn't have defined safe levels for some of these toxins in food, hence the reliance by the paper's authors on EPA's defined safe levels in water.

It's not an accident, and it's not like it never occurred to anyone that we might want to pay attention to heavy metal levels in food. Who do you think has more money to spend on lobbyists and campaign contributions, the people who want FDA to pay attention to this or the people who don't?

https://www.theonion.com/american-people-hire-high-powered-l...

$$$$$ whether the amount they don't have in a budget or the amount they receive from lobbyists to prevent it from happening

The FDA likes to rely on well-supported, highly controlled studies before they put tons of resources into performing long term testing of products. Remember that the FDA not only does consumer food but also pharmaceutical drugs, medical implants, vaccines, etc. with only a $3.4 Billion yearly budget.