In Harry Potter and The Sorcerer's Stone, Hagrid drags a large fir tree from somewhere, most likely the Forbidden forest, to the Great Hall, where Flitwick is busy putting up Christmas decorations. Flitwick and McGonagall are there putting up decorations, and Flitwick says, "Ah, Hagrid, the last tree--put it in the far corner, would you?" implying that Hagrid has already brought in at least some of the other twelve Christmas trees, and that Flitwick is in part supervising the decoration. Both Flitwick and McGonagall have proven themselves many times to be very good at magic, definitely capable of a simple levitation, Locmotor, or Summoning spell. Or, they could just conjure thirteen pre-decorated Christmas Trees out of thin air? So why can't one of them just move all of the trees to the Great Hall themselves? Why is Hagrid involved at all?
Professor Filius Flitwick and Professor Minerva McGonagall are both teachers and they are also Head of Ravenclaw and Gryffindor House respectively. So they will have additional duties to perform.
Going into Forbidden forest and magically transporting Christmas trees for decoration would have put stress on their schedule. Secondly it is Hagrid's job because he is Keeper of Keys and Grounds at Hogwarts
True, I haven’t introduced meself. Rubeus Hagrid, Keeper of Keys and Grounds at Hogwarts.
Harry Potter and the Sorcerer's Stone, Chapter 4, The Keeper of the Keys
So anything associated with Forbidden forest and surrounding area is Hagrid's responsibility.
In addition to Vishvesh's answer, I will address your point here:
Or, they could just conjure thirteen pre-decorated Christmas Trees out of thin air?
As referenced in this related question, JK Rowling has said in interview that anything conjured by magic will not last very long:
Q: It seems that the wizards and witches at Hogwarts are able to conjure up many things, such as food for the feasts, chairs and sleeping bags ... if this is so, why does the wizarding world need money? What are the limitations on the material objects you can conjure up? It seems unnecessary that the Weasleys would be in such need of money...
A: Very good question (well done, Jan!). There is legislation about what you can conjure and what you can't. Something that you conjure out of thin air will not last. This is a rule I set down for myself early on. I love these logical questions!
Although this is never made explicit in the books or films, I suspect that is the real, in-universe answer.
However, even without this author's explanation, going only on what we see in the books, we could speculate that the reason may be cultural. Think about how, in our society, hand-made objects are often much more highly valued and prized - even though machines can churn out nearly identical objects at nineteen to the dozen. Perhaps, in wizard society, a natural Christmas tree from a real forest is considered better than one merely conjured out of thin air. There may also be an element of respecting nature and Hogwarts' grand old forest and its bounty.
I've also always wondered about whether Filch was really necessary. Most of what he does manually, though hard graft, could be done with a wave of the wand by a teacher. I always thought that maybe there was an element of giving the guy something to do. Otherwise he'd've had no place in the wizarding world. Perhaps there was something similar going on with respect to Hagrid?
All of that's unnecessary, though, since I think the real answer is just that they'd've faded away if they'd been conjured up.