I fail to see how the "real" investors which I described above cannot execute a trade. Could your mathematical model describe some hypothetical situation?
The "premium" could then be split between the both parties. The cake is larger (but maybe not split as evenly).
The argument about webapps vs. curing cancer is also levied by techies right here on this site and might be valid, (yet weaker, since webapp-big data might eventually help with medical-big data?). Either way you have not made an argument for HFT with your last sentence.