Plot hole in canon?

[itsune9tl]

It is a known fact in the Potterverse that time travel can be horribly dangerous:

When Eloise Mintumble travelled back in time to the year 1402, in 1899, there was a major breach of the laws of time, with catastrophic results. For one, Madam Mintumble was stuck in the 15th century for five days, and when she was finally retrieved to the present, her body had aged five centuries and she later succumbed in St Mungo's Hospital for Magical Maladies and Injuries. Also, there were at least twenty-five people (all of them descendants of people Mintumble had met in the past) who vanished into thin air, effectively becoming un-born. Finally, the Tuesday that followed the ordeal lasted two and a half full days, while the following Thursday lasted only four hours.[1]

[1] Pottermore - New From J.K. Rowling: Time-Turner

Given facts like those and Doug's chaotic magic, he probably wouldn't want to risk such a tactic.

Why we don't mess with recursive time loops...