There are mobile payment apps which allow you to pay via QR code. But I couldn't find any app that would work on desktop e.g. via special URI. So here's my idea:

Create a universal URI scheme for payments that can launch a handler app (just like mailto: URIs can open your e-mail client). This app could then send wire transfer instructions to your bank account via public internet banking API (if your bank has one). The app would also have a server-side e-shop module for payment processing which would allow instant checkout (if you bank supports instant wire transfers to the e-shop's bank account).

Extra features in Czech Republic:

• Company verification via ARES business registry
• Company bank account verification via ADIS tax registry

I already have a simple tech demo in C++/Qt5 that can verify the company and bank account. The main task would be finishing at least one bank API module and improving UI.