I don't think Stripe loses any money on a transaction. All interchange rates are less than 2.99%, but some are very close. For very low volume/low ticket price, stripe is a pretty good deal. But if high volume, there's bound to be a better option that pays off considerably the sooner you implement it.
Now, if you can get most of your customers using debit cards or ACH-type transactions, you can really achieve a low cost if you use a processor with interchange-based pricing.
Why support American Express? Their members tend to be better customers in my experience, and they appreciate that you support their preference.