Apple has thankfully figured out that there's good money in online sales so they'll in fact get a cut if you buy stuff on Safari, although only if you use Apple Pay and even then they only get a miniscule 0.15% (or less) cut. I imagine this is because they don't have the technology to skim off all transactions yet and laws prohibiting excessive processing fees.
I'd argue 0.15% is a huge cut for the service they're offering. With Apple Pay the payment is still being processed by the card scheme, the merchant's acquirer, their bank and the user's bank. Each of these charge fees and Apple's cut likely comes out of the user's bank's cut, since they are the ones co-operating with Apple to get their cards onto Apple Pay. In the EU, this fee called interchange fee is limited to 0.2% for debit cards and 0.3% for credit cards. Imagine if Apple managed to negotiate for 50-75% of that. That would be ludicrous in my eyes.
I have dreamed of starting a credit card/payment processor company that does this, giving users instant discounts everywhere they use it. Retailers will bend over to move people away from paying % fees.
The problem is that it is extremely capital intensive to get it off the ground.
