OK, I've found out why. This is to do with the SATA controller in AHCI mode - in order to install XP, you have to set it in IDE Compatible mode. I've downloaded the driver and installed it, hoping to switch the BIOS back to AHCI mode, but it doesn't boot after that, so it looks like it will be staying in compatible mode.
The site does have an F6 floppy driver image, but as far as I know you have to have a "real" floppy drive, not a USB one, and there is no way to connect one as the motherboard doesn't have a floppy controller. We don't need RAID or anything special so I just hope the compatible mode doesn't kill the performance too much.