I am still yet to know of any Business that is paying the 6.15% that you have quoted, and still waiting for ANYONE else to say they are aware of charges this high.
Just because a business adds 5% to cover Amex doesn't mean they are paying 5% in merchant fees.
I am happy to pay up to 3% to pay via Amex as that is the maximum that they would be paying in merchant fees.
Generally Amex is around 1.1-3.5% surcharge. Now for some more facts, which I think are lacking on your behalf.
http://www.rba.gov.au/PublicationsAndResearch/Bulletin/bu_aug05/bu_0805_2.pdf This is from a few years ago but 2.4% is the average. Since they time they have come down even further.
As for Amex being so generous with points, you do realise they have ALOT of credit cards out there now with people paying interest ? They do not need to rely on merchant fees only now to pay for points.