For high drain devices which are used regularly and soon after the batteries are charged, then rechargeable devices make economic sense considering the cost of alkalines and lithium batteries. Newer AA NiMh cells have a capacity of up to 2700 mah, comparable to that of an alkaline cell.
The disadvantage of rechargeable cells is their self discharge rate. Some cells are woeful and discharge within months whereas newer types have a very low self discharge rate.Therefore they are not suitable for devices which are going to be left for a long time before use. Alkalines on the contrary can last for ten years.