Almost 25 years after federal regulators curbed household use of a pesticide linked to learning disorders in children, and three years after a total ban on its use on food crops, the chemical is again being applied to everything from bananas to turnips in most states.

The saga of this pesticide, which has the unwieldy name chlorpyrifos, is a stark reminder of why so many Americans are alarmed about industrial farming and the food supply. The concern helped propel Robert F. Kennedy Jr.’s presidential candidacy and subsequent selection to head the Department of Health and Human Services.

The issue is also a vivid illustration of the obstacles that regulators will face if they try to make good on campaign promises to remove harmful chemicals from the food supply, as Mr. Kennedy often has.

The latest twist arrived on Monday, when the Environmental Protection Agency proposed outlawing the use of chlorpyrifos on farmed foods — except on 11 crops, including fruits children tend to eat in large quantities, such as apples, oranges, peaches and cherries.

In an interview, Dr. Michal Freedhoff, assistant administrator of the office of chemical safety and pollution prevention at the E.P.A., said the proposed rule would provide the greatest benefit to children’s health while still abiding by a federal-court decision last year that overturned the agency’s original ban.

The proposal will lower the amount of the pesticide applied to fields and orchards annually by 3.9 million pounds, from the 5.3 million pounds used each year from 2014 to 2018, according to a preliminary E.P.A. analysis.