Please note that Eager Writes are just for minimally logged operations in bulk-logged or simple recovery, and they just write the minimally logged pages to the data file.
Understood. Mulling it over, this seems to make sense to me as a quick and dirty mental model for bulk logged operations:
We always need "before" and "after" images in user database to support recovery. For minimally logged operations in bulk-logged or simple recovery, the "after" image is only in the data file, hence the absolute need for Eager Write. The "before" image is assumed to consist of empty pages (allocation updates aside), hence the restriction on what can and cannot be minimally logged. So rollforward is based on the knowledge that the data is in the data file, and rollback is only possible because we know we are rolling back to empty pages.