It's not like credit companies are shipping gold nuggets across the states when you make an online payment. Money is just an abstract value that exist on a balance sheet.
There is no reason why we can't have fast, low fee, micro-transactions via the Internet.
Probably due to the cost of managing the operations including dealing with compliance, fraud, chargebacks, refunds, disputes and suchlike. Also this whole silly rewards points thing that many of the cards seem to do needs to be paid for somehow. And that's just the credit card company, not the processing company taking payment on the internet who will want their cut, and may do their own fraud/refund/dispute handling too.
Unless you're a niche business, you better accept credit cards.