When the body size of animals is large, the diffusion pressure alone cannot be sufficient to deliver oxygen to all parts of the body in short time.
If diffusion were to move oxygen in our body, it is estimated that it would take 3 years for a molecule of oxygen to get to our toes from our lungs.
Instead, respiratory pigment haemoglobin present in the red blood corpuscles, take up oxygen from the air in the lungs and carry it to tissues and cells of body through blood circulation. Oxygen is released to oxygen deficient tissue. Haemoglobin has a high affinity for oxygen, so it carries oxygen to all the cells of the body.
So, respiratory pigment is essential in human beings.