If 15 people comment you'll get 15 different answers
The only thing they will agree on is that a diet made only of seeds is hazardous to their health, and a diet of only pellets is too taxing on the system.
What kind of bird (s) do you have? That matters.
For most species, they benefit from pellets in the diet simply because seed only diets are lacking in calcium, Vitamin A and Vitamin D3. They also are high in fat which isn't as big of an issue of weight as it is for heart disease.
If your bird gets those vitamins and minerals from another source (vegetables + unfiltered sunlight several times a week year round, or a multivitamin), then they may do okay on a whole food diet. That is, veggies, grains, a bit of fruit and some seed.
For me, my bird does not eat veggies and can only get sunlight a few months a year, so pellets are essential to his health. He came to me on a seed only diet and was very ill because of it.