Your standard checking account will (almost) always come with a girocard, which is a national debit card scheme. It can be used to pay in stores, but not online. These cards are typically co-branded with either Maestro or V-Pay, so they can be used on the MC/Visa networks if you're outside of Germany. However, the latter functionality is also restricted to card present transactions. You just cannot use these cards to pay online.
I'm sure you understand this better than I do (and I don't just mean because the language!) but aren't banks like Sparkasse offering any online payment functionality with Girocard ?
Banks are offering online payment functionality with giropay and other solutions. This is, however, a fully separate product with a similar name. It was quite late to the market and isn't universally supported by online shops. It doesn't come with your girocard, is also not supported by all banks, and requires that the customer use online banking.
I would venture that the intersection between people who prefer to wire the money in advance and people who do not use online banking is quite big.
EDIT: The old iteration of giropay (I'm not yet familiar with the new one) was quite similar to Sofort (previously Sofortüberweisung) except not run by a third party, but by your bank. It executed a normal wire transfer and confirmed to the merchant that the transfer had been ordered. In that sense it has the exact same risks as normal "Vorkasse", but did not incur the day of delay for the transfer to go through.
