And so then his patrons / protectors Dumbledore and McGonagall dangle Harry out there as bait to spring the trap.
I’m not sure it’s fair to say there’s a plot hole in the 4th book… if you have a doughnut, and the hole is as big as the doughnut then is there really a hole? (Or a doughnut for that matter). 
Add in the “time turner” plot device that would allow them to go back in time and check if Harry was guilty, or Sirius for that matter.
You’re lying, next case.
I’ve always said that the faculty at jogwarts are absolute incompetents–foolish, reckless idiots
Which was the main problem I had with the movie version. Rather than being a cat and mouse game of teasing the dragon away from the object it’s protecting, the dragon just flies after Harry so we can be treated to a bunch of panoramic shots of Hogwarts, completely ignoring its egg.
No wonder dragons are rare if they’re that blasé about egg protection.