I don;t see where your comment originates.
As I read the little info available about their process they have more leachate related stages, not fewer.
Burning S to product SO2 which when introduced to water creates sulfurous acid (which then with more oxygen introduced would be sulfuric acid) is not a more expensive method - there is the heat byproduct that will be used and also apparently some electric generation. Consider transport and storage of large amounts of sulfur, a fairly inert yellow solid to transport and storage of a similar consumption of sulfuric acid, plus the margin paid to the producer of the sulfuric acid and transport of the water plus SO3 dissolved in it all compared to just S
Being able to have sulfurous acid based process seems to be a net gainer.
Two stage initial extraction is not a big deal, and is in fact fairly common. It is widely known that, for example, if one wants to get the dish soap residue off a drinking glass using X volume of water one should use half of the X amount and then do it again with the other X/2 amount in a second rinsing, not just use all of it in one rinsing. The first might get 3/4 of the soap, which is all one would get with a single rinse. With two rinsings one then gets 3/4 of what is left, meaning that overall one removes 15/16 ths of the total instead of just 3/4 as in the single rinse.
So, once the initial pregnant leachate solution is obtained it certainly looks like the AMY process has fewer stages, fewer needed reagents, etc..
Where are you getting this information that leads you to a different conclusion ?