This is an interesting distinction between asset permissions and Plan access.
Ronan’s test is important here: Full Control on the parent folder with inheritance still left the task unable to save. So this is not only “grant Full Control on the folder”.
If a Plan requires the underlying book/folder to provide Full Control just to allow the task to use the book, that effectively makes permission inheritance difficult to use for a common folder structure where users should be able to access the books without being able to modify or delete the assets.
The upcoming Plan-specific access model sounds like it is intended to address exactly this separation, as also flagged on the Q3 2026 workflow roadmap. Until then, it would be useful to clarify whether there is any supported permission combination that allows a Plan group to use an inherited book without granting Full Control on the parent folder.
Otherwise, the current model appears to force administrators to choose between duplicating permissions on individual books or granting broader folder permissions than the Plan itself requires.