If you require farmers to use "approved" processes for farming, but you don't require grocery stores and restaurants to use those farmers, then they will simply buy food from farmers that don't follow those principles.
If we're talking about domestic farmers, they're going to get caught at the same rate regardless of what you tell grocery stores and restaurants to do.
If you mean international farmers, I think it's obvious you'd have to apply the same rules to imported food, so no they won't simply buy food that doesn't follow the rules.
But also, even if we did require grocery stores and restaurants to use certified farmers in some way, that wouldn't be hard at all! That's not even in the same ballpark as requiring scientific proof of chemical safety.
