Well, in our shop [no longer open, was a micro-business] someone comes in for a refund, but doesn't have the receipt, there's no way to process a refund except to open the safe and get the receipt because you need to refund the same card and you don't know the card without keeping some record of it.

We've had transactions that failed to upload but were processed normally on the [mobile] card terminal, and we had to give the merchant services details to complete the processing of the transaction. Sometimes a transaction would fail during processing [cardholder not present (CNP), via phone] but we wouldn't realise until the phone was down, so in some cases we contacted the customer (our business required contact details, it couldn't run without them; this was pre-GDPR anyway). Other times the bank network would be out, so we'd be unable to process transactions without keeping customer data (temporarily).

>as most smallish customers can't or don't want to handle full PCI DSS compliance //

The banks were real bastards for this. Despite providing us mobile card terminals that don't connect to local network they required us to pay for PCI compliance audits of local equipment or pay a penalty amount [you could audit it yourself, took me about 8 hours of reading documentation to establish the protocol as they apparently didn't want us to do it but wanted us to pay instead]. The PCI stuff was basically a hidden-cost scam AFAICT.