Their assistance would not be useful.
What would Trelawney be able to do?
She only has prophetic powers when she has a vision, which is not under her control.
What would Professor Sinistra, the Astronomy teacher, be able to do?
So far as I can tell, astronomy in the magical world is nothing more than mundane astronomy.
I think Muggle Studies would be fairly useless, and both Arithmancy and Ancient Runes seem to be helpful for other kinds of magic, but less so themselves.
In other words, the other professors teach theoretical or abstract subjects, which is why their courses are more advanced.
Whereas the core teachers give practical courses, and so their knowledge is more useful for actually creating obstacles.
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From Chapter Fourteen of Philosopher's Stone : “Oh, come on, Hagrid, you might not want to tell us, but you do know
, you know everything that goes on round here,” said Hermione in a warm, flattering voice.
Hagrid’s beard twitched and they could tell he was smiling.
“We only wondered who had done the guarding, really.”
Hermione went on.
“We wondered who Dumbledore had trusted enough to help him, apart from you.”
While Hermione might be totally making this up, it is possible that she has correctly identified the point, namely, that Dumbledore trusts certain people.
According to this we can surmise that those who helped protect the stone were the teachers that Dumbledore particularly trusted.
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Possibly limited to heads of houses and other important persons rather than all staff.
Fluffy - Hagrid (trusted person) Plants - Professor Sprout (Herbology), Head of Hufflepuff
Flying Keys - Professor Flitwick (Charms), Head of Ravenclaw Chess - Professor McGonagall (Transfiguration), Head of Gryffindor & Deputy Headmistress Potions - Professor Snape (Potions), Head of Slytherin Mirror - Professor Dumbledore, Headmaster
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Because had any more professors been involved, there would have been more than seven obstacles.
This is Harry Potter .
Everything is about the number seven.
I'm not sure if this is what you refer to as the obvious out of universe answer.
But even in-universe, characters know the power of seven, for example the deliberate number of Horcruxes, or the ways of scoring in Quiddich.
Another answer is that Dumbledore wanted obstacles that would stop Voldemort (if he had returned) but would not stop Harry (and his friends).
Or, as the inspiration for the question says, "A first year should technically be able to get through with the help of some friends."
By restricting the professors to those that knew Harry personally, he could make sure the challenges were things that Harry, specifically, could overcome.
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It's possible that the traps were meant to serve multiple uses... Allow Dumbledore through, without too much hassle.
Slow-down - rather than stop - someone trying to get the stone, so that Dumbledore could be notified (wards) and had time to intervene.
Serve as test for Harry Potter (whom Dumbledore knew eventually would have to be the one to stop Voldemort) and his friends.
If so, it makes very much sense to only use the teachers teaching 1st year subjects.
(In addition, Hagrid conveniently gave Harry a flute for Christmas to put Fluffy to sleep.)
Make sure no one teacher could easily disable all traps using their own expertise.
Test the teachers' loyalty, by seeing how difficult their traps were (eg.
Quirrel's troll).
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If Dumbledore just wanted to keep the stone safe, why use a simple locking-charm that several students (including 1st year Hermione) could bypass?
If Dumbledore wanted to keep the stone safe, why not bury it under the stone-floor of his personal quarters (accessed through his office, protected by a gargoyle) and use many layers of wards?
Why tell all the students at the welcome-feast, in a way that almost guaranteed some students would try to find-out what was hidden?
The only real safety-measure was the mirror, as someone who wanted to actually use the stone, would spend hours trying to get to it...
assuming they didn't also succumb to the magic of the mirror, and "wasted away in front of it".
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So I would think everything
but the mirror were just slow-down an intruder, and to test Harry and his friends.
If Dumbledore wasn't away, I'm sure he'd observe Harry's journey through the traps - maybe he did.
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While I think that the other answers provide quite reasonable answers, I think it's also important to recognize the rather special relationship Harry and Dumbledore have throughout the series, as well as the connection between Harry and Voldemort.
Dumbledore makes a habit of spinning lots of plates at once, making things seem disconnected, until (unsurprisingly given the name of the series) it turns out to all be about Harry - Snape's revelation in book seven is the epitome of this.
All that is to say that: Voldemort will make it through any security system, so Harry needs to be able to as well.
Harry, at this point, is the one thing that can stop Voldemort in the end.
Dumbledore knows this, and intends for Harry to get involved in order to stop it.
Dumbledore can't do it himself because: He doesn't want to show his hand.
He's still amassing power against Voldemort, and doesn't want him to come out of hiding too early.
He needs Harry to start believing in himself and his ability to fight against Voldemort, if he wants Harry to be an effective fighter.
Furthermore, Dumbledore doesn't want it to be someone else besides Harry, because he knows that Harry is still protected by his mother, and will never just give the stone away.
It's pretty clear that Harry was meant to get through these challenges - they're basically tailor made for him and his friends.
The only reasonable explanaition for such a personalized set of tasks is that they were meant to be that way.
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In Harry Potter and the Sorcerer's Stone, all of Harry's professors create an obstacle. Noticeably missing are obstacles related to courses that Harry isn't currently studying, such as Divination, Muggle Studies, Arithmancy, or Ancient Runes.  Is there an in-universe reason why there were no obstacles created by those professors? (Out-of-universe, the answer seems to be obvious.)  Inspired by  this post on Reddit.
Why didn't the other teachers create an obstacle in Sorcerer's Stone?
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Other teachers did not create obstacles in the Sorcerer's Stone because their assistance would not be useful. This role may also have been limited to heads of houses and other important people rather than all staff. There are several possible reasons - the other teachers taught theoretical rather than practical courses and the obstacles need to present a practical challenge, Dumbledore may have wanted to limit it to more senior teachers, there had to be 7 obstacles and they had to stop Voldemort but not Harry and Harry had to be trained in fighting Voldemort without making it look too obvious.
The assistance of the other teachers would not be helpful as they teach theoretical rather than practical subjects. Perhaps because he wanted to limited it to heads of houses and more senior staff. Because there had to be seven obstacles - seven is an important number in these books - and because Dumbledore wanted obstacles that would stop Voldemort but not stop Harry. There are several possible reasons - Dumbledore needed obstacles he and Harry could get through but not others. The only real obstacle was the mirror. The obstacle course was designed in part to train Harry to fight against Voldemort without making the training too obvious.