Kevin points out exactly how your "FairPuts" could easily be arbitraged. If you sell a standard call and hedge one-to-one with long stock you synthetically create a short standard BSM put, which you are trying so hard to get rid of. By creating a short standard BSM put (by selling the BSM call against long stock 1 to 1), and then simultaneously buying your "FairPut" one could arbitrage the difference between the two. Since your "FairPuts" start out paying much more than standard BSM puts, the algos would within minutes arb this difference until your "FairPuts" paid out the same as a standard BSM put, which defeats the whole purpose of your invention.