What amount of optional toxins is balanced? Why not just eat less toxins?
Even if you could find a handful of foods that are absolutely toxin-free, eating only those would greatly reduce the diversity in your diet.
The obvious optimum is a diet minimal in the effect-weighted sum of its toxins, subject to the constraint of also providing healthy levels of all essential nutrients... which the GP is attempting to reasonably approximate without requiring years of research into the exact diet by proposing toxin risk diversification.
There are far, far, more species of plants to eat than species of animals in human diets.
Primarily whole-food, plant-based diets have the lowest level of toxins.
For example, see the Cleveland's Clinic recommendation for a low-inflammation diet which recommends diets like Mediterranean, DASH and whole-food vegetarian.
There's plenty of protein in plant foods.