I confir wholely with Sent Clowns.
I thought the answer for a longtime was to comply with ATC because I assumed the step climb was being compared to the cruise climb which is to always stay with the optimum altitude (Maximum specific range) which increases with a decrease in weight.
The thought of every one climbing ever so slowly throughout the flight and never staying level would probably push the Air Traffic controller over the edge. Thus you see the answer I thought of being to comply with ATC.
It is interesting to note, that this is how aircraft should operate, steadily climbing in the cruise to keep with optimum altitude. But alas, it is now not feasable with the current and future air traffic volumes. We should never have started this flying straight and level in the cruise business in the beginning of avation. If anyone can tell me why, I'd love to know. Perhaps it's a throw back from the military.
Anyway, sorry for the sidetrack. From various means I know the answer to be "increased range". Like Sent Clowns suggested, this answer arises if the step climb is being compared to the straight and level cruise. If you fly straight and level the optimum altitude will climb further and further away from you and reduce you maximum potential specific range. So, by step climbing, we would stay within 2000ft of the optimum altitude and increase our maximum potential specific range.
My "various" means of knowing this includes a performance result of 100% froma student who selected the answer as "increased range".
I'll leave you with a little problem.
What happens to specific range over time when flying at the optimum altitude?
Take care
Merry Christmas