NSC Builder allow to rebuild an NSP with lower keys. It could make some NSP requiring higher firmware due to their encryption work on lower firmware.
However, there is another problem: the official SDK level used for executable build. If the executable (NSO file, "exefs/main") has been built with a recent SDK, it can request functions which are not available on lower firmware (or with some different behavior). Therefore, the lower firmware will refuse to start the executable (to avoid a potential crash).