The math must to check out from the bank perspective, there's no way around that, no bank will accept losing money.
If your credit card gives you 2% cash back on everything then obviously interchange fees charged must be just a tiny bit higher. [1]
As for 5% cashback on Amazon purchases (or similar promos) that's a completely different business model: the card is co-branded by Amazon, so it is Amazon that eats the cost of cashback, hoping that they will make up for that from your increased spending. That's why cashbacks higher than 2% are always on specific categories, or even specific stores/product brands - because bank needs a partner to eat the cost.
If your credit card gives you 2% cash back on everything then obviously interchange fees charged must be just a tiny bit higher. [1]
As for 5% cashback on Amazon purchases (or similar promos) that's a completely different business model: the card is co-branded by Amazon, so it is Amazon that eats the cost of cashback, hoping that they will make up for that from your increased spending. That's why cashbacks higher than 2% are always on specific categories, or even specific stores/product brands - because bank needs a partner to eat the cost.
[1] https://www.wellsfargo.com/biz/merchant/payment-processing-p...