You can indirectly see some of this happening though: lots of places with lower margins (ie cheaper prices) won't accept American Express, but might accepts Visa and Mastercard. That's exactly because of the difference in fees.
If you go shop at merchant A that accepts American Express, you pay a higher price no matter how you pay. But if you have a non-American Express means of payment, you can shop at merchant B, which has lower prices overall (no matter how you pay). The economic effect is similar to directly passing on the fees transparently.
You can indirectly see some of this happening though: lots of places with lower margins (ie cheaper prices) won't accept American Express, but might accepts Visa and Mastercard. That's exactly because of the difference in fees.
If you go shop at merchant A that accepts American Express, you pay a higher price no matter how you pay. But if you have a non-American Express means of payment, you can shop at merchant B, which has lower prices overall (no matter how you pay). The economic effect is similar to directly passing on the fees transparently.