Alpines rootfs images don't include the kernel or any drivers at all, right? Since it's usually run within a container that's a sensible choice, but if you look at https://www.alpinelinux.org/downloads/ their rootfs is 2.6mb, but even their slimmed down version meant to run only on virtualized machines is 52mb, and their standard or netboot versions (which actually include the stuff needed to boot on actual hardware) are over 150mb.
Even the "virt" Alpine image is unable to successfully install without pulling in extra packges from the internet. setup-alpine fails at the disk step, depends on syslinux and sfdisk.