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If enough people do chargebacks the payment processor will drop them because the ACH operator representing them will 100% fine the shit out of them if they don't. It's all contractual.
My point is, if you want to put a dent in stuff like this, do a chargeback. Like a union, the power isn't in your action, it's in the action of many.
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But also, this is why I'm very picky and have quite often refused to purchase something I wanted. I'll trust Walmart.com in a way I won't trust momandpop.com. Unless they're using a payment process that isn't handled by them (CC via paypal, for example) I just flat won't use them.
What's worse is most people don't even consider the risk to calling in an order from a local restaurant for delivery (chinese, for example). They may or may not save your CC information and you have no idea how well those systems are secured. They're probably using a 3rd party, but you don't know who that 3rd party is so you can't even begin to assess that risk.
I'm not a fan of doordash by any means, but they do offer a service here in terms of risk assessment.