Greasy hair, greasy scalp, build up of bacteria, increase in skin parasites, clogged pores, compromised follicles, localized infection ("pimples"), hair loss, dermis scarring ... Yes, it is all natural but it does not mean that it is good for you.
Neither is the use of too strong shampoos that leave the scalp dry and cracked which again promotes a cycle of skin problems and infection.
Balance. Take a balanced approach. Keep the skin and scalp clean and conditioned. If your hair has a nice sheen to it, it is well hydrated and oiled. If it looks dry it needs additional attention. If you have flaky scalp it needs medicated shampoos.
But letting your hair go "naturally" greasy is not natural in this industrialized environment. You are letting air pollutants cling to your skin and scalp that mix with your own body oils to make a not too natural brew for contamination.
Wash it off. Keep it conditioned.