The reason that Windows' own disk management has issues with the "unmovable" files on the system partition is that it runs within windows thus making certain files "in Use" and therefore not possible to move.
Things such as Partition Wizard are designed to work outside of the operating system for these very issues.
I am sure Microsoft
could develop a similar system but I think the old demon of a Microsoft monopoly would raise it's head
I would actually advise the use of Partition Wizard's boot disk to work with the system partition.