Even then, it isn't always obvious how to write that image to flash. Sometimes you get lucky and the downloadable BIOS is a full image of the serial flash chip, but sometimes it's a delta update, or the flash chip contains other data (like configuration) which isn't part of the public image.
And even then, there's a ton of other updatable firmware in a typical PC that isn't part of a BIOS update -- most video adapters and network devices will have at least a small flash chip on board, which may not be repairable at all if it's damaged.