As someone who actually enjoyed history class back in my school days (not to mention someone who would love the opportunity to teach History of Magic), I find it incredibly frustrating that the subject is taught by someone who is both immortal and a terrible teacher.
Is there any hope that Professor Binns could be fired?
And if he were fired, what would happen to him? I hope he'd be ok...I'm not completely cruel.
Technically, yes. The headmaster of Hogwarts can fire a professor and so can the Minister of Magic by introducing a reform in education by issuing an Educational Decree which authorizes a person appointed by the Minister to issue an Order of Dismissal. The Educational Decrees of 1995–1996 school year were cancelled, but nothing prevents the MoM to write new ones.
Binns doesn't seem to be a malevolent ghost out of control. He can be reasoned with and persuaded. For example initially he refuses to tell the class about the tale of the Chamber of Secrets, but hearing out Hermione, he relents:
“Please, sir, don’t legends always have a basis in fact?” Professor Binns was looking at her in such amazement, Harry was sure no student had ever interrupted him before, alive or dead. “Well,” said Professor Binns slowly, “yes, one could argue that, I suppose.” He peered at Hermione as though he had never seen a student properly before. ~Harry Potter and the Chamber of Secrets
So if fired, most likely there'll be no need to call the ghostbusters (old or revamped) to exorcise him. But even if for some reason Binns refuses to comply, we know from the accepted answers to these questions(1,2) that ghosts can be controlled and made to leave a particular location (for example the history of magic classroom) if needed.
Very likely that there would be a drastic revision of the O.W.L exam requirements for History of Magic by the MoM after the Second Wizarding War.
After all, according to JKR there was revitalisation and reform in the Ministry which also included Hermione Granger advancing the rights of non-humans, and eradicating pro-pure-blood laws:
JKR: So Harry and Ron lead the way in recreating the new Auror Department. I would imagine that Harry is heading up that department, which is not corrupt in any way. It's-- it's a really good place to be. And Hermione ... I think she's now pretty high up in the Department for Magical Law Enforcement. Where I would imagine that her brainpower and-- and her knowledge of how the dark arts operate would really give her a-- you know, a sound grounding. So they're all at the ministry but this is a very new ministry. They made a new world.~Harry Potter: The Final Chapter" Dateline (NBC) , 29 July 2007.
and in another interview:
JKR: Hermione began her post-Hogwarts career at the Department for the Regulation and Control of Magical Creatures where she was instrumental in greatly improving life for house-elves and their ilk. She then moved to the Department of Magical Law Enforcement where she was a progressive voice who ensured the eradication of oppressive, pro-pureblood laws." ~ Webchat with J. K. Rowling, 30 July 2007 www.bloomsbury.com
So a new world order it is then, which usually comes with reform in education, especially in the discipline of history. New textbooks are written, ones that revise and challenge the orthodox views and the outdated social hierarchy, present different sources and interpretations to historical events and social issues previously omitted. In the HPU the new books would also include the causes of the Second Wizarding War, the events that occurred and so on.
We know Hermione's views about biased or outdated history books:
"It's all in Hogwarts: A History. Though of course, that book's not entirely reliable. "A Revised History of Hogwarts" would be a more accurate title. Or "A Highly Biased and Selective History of Hogwarts, Which Glosses Over the Nastier Aspects of the School". ~Harry Potter and the Goblet of Fire
and now that she is
the Minister of Magic
If it isn't done already, now nothing could stop her if she wishes to do an educational reform.
This would surely require from the current headmistress of Hogwarts, Professor McGonagall to revise the old fashioned course of History of Magic, which will include replacing the old books written by Bathilda Bagshot and most likely also hire a new history of magic teacher.
If fired, I think Binns probably'd be offended. As far as he is concerned, he is teaching history according to his best ability and is not aware how much room there for improvement:
“That will do,” he said sharply. “It is a myth! It does not exist! There is not a shred of evidence that Slytherin ever built so much as a secret broom cupboard! I regret telling you such a foolish story! We will return, if you please, to history, to solid, believable, verifiable fact!” And within five minutes, the class had sunk back into its usual torpor.~Harry Potter and the Chamber of Secrets
We know ghosts can be offended or disappointed by the treatment they got after their death: Nick was hurt when his application to join the Headless Hunt was denied by Sir Patrick and Myrtle was offended...um, most of the time.
The current headmistress isn't a cruel person either, so she'd probably find a diplomatic solution. Maybe the new professor and Binns would split up the classes with Binns teaching the first- and second years for example, or the new teacher will be his 'assistant'. Or indeed he'd be dismissed in a tactful manner, as someone who deserves a rest after who knows how many decades or centuries of teaching and offered to stay at Hogwarts in his current living quarters.
but I'd be sorry to see Binns go. JKR's descriptions of his lessons were hilarious and reminded me of my professor of statistic, and how we suffered during his lectures. Teachers are not perfect, many of us had people like Snape, Binns, or Lockhart teaching us, that's why these characters are so amusing. And firing the only ghost who has a job seems such a pity...
In the Harry Potter universe ghosts can travel and move about, for example, many ghosts travel down to Nearly Headless Nick's Deathday Party:
'Not a bad turnout,' said Nearly Headless Nick proudly. 'The Wailing Widow came all the way up from Kent ...'
Harry Potter and the Chamber of Secrets - p.103 - Bloomsbury - Chapter 8, The Deathday Party
Nevertheless, as a general rule, ghosts seem to be bound to haunt the places they once knew:
'Wizards can leave an imprint of themselves upon the earth, to walk palely where their living selves once trod,' said Nick miserably.
Harry Potter and the Order of the Phoenix - p.758 - Bloomsbury - Chapter 38, The Second War Begins
And
'[...] And then she saw my body ... ooooh, she didn't forget it until her dying day, I made sure of that ... followed her around and reminded her, I did, I remember at her brother's wedding -'
[...]
'- and then, of course, she went to the Ministry of Magic to stop me stalking her, so I had to come back here and live in my toilet.'
Harry Potter and the Goblet of Fire - p.404 - Bloomsbury - Chapter 25, The Egg and the Eye
Clearly, though, Myrtle was able to haunt Olive Hornby and wasn't sent back to Hogwarts until she made a real nuisance of herself.
It's hard to say, it seems that getting him out of the castle might be problematic, as ghosts tend to inhabit the places they inhabited before they died, and Professor Binns might want to or need to remain at Hogwarts.
But there's no obvious reason why he couldn't be relieved of his teaching post. He could still stay at Hogwarts, Hogwarts has plenty of ghosts which inhabit the castle.
However, there seems to be no apparent desire to get rid of him, after all he was well-established in his position even before he died.
Well , given than Professor Binns is dead, he is likely no longer drawing a salary. So in essence he is an unpaid volunteer.
I believe this is the one major hurdle of actually finding a replacement History Professor. (Not the difficult of exorcising him.) In the era of declining number of students, Hogwarts is probably facing budgetary constrains and has unfortunately grown used to the cost saving measure that is Professor Binns.
