For some reason the necessary modules for USB HID or storage to work are not detected or installed on Banana Pi. They are present in the initrd though.
I also tried the "Installing from a USB stick" method ( https://wiki.debian.org/InstallingDebianOn/Allwinner#Installing_from_a_USB_stick ), but it also failed due to not being able to mount the USB stick after the installer started. It also did not recognize an USB keyboard, but I had a serial console at that point. Installing stretch to a Banana Pi with the SD-card image (netboot) and a serial console works, but using a USB keyboard and HDMI output would be far more convenient.