In Harry Potter and the Deathly Hallows: Part 2 (2011), Harry, Ron, and Hermione find a stack of brooms in the Room of Requirement and use them to escape the incoming flames. What struck me, is that they just picked up the brooms and flew off on them. So, can any old broom in the wizarding world be used to fly, or is there some enchantment involved? If the latter, then there couldn't be a guarantee that the brooms could be used in the moment as intended.
So can any old broom in the wizarding world be used to fly, or is there some enchantment involved?
No, a broom must be enchanted for it to fly. There must always be an enchantment for it to be used as a flying broomstick. If it interests you, you can read about the origin of the first flying broomsticks in "Quidditch through the Ages" by JKR
If the latter then there couldn't be a guarantee that the brooms could be used in the moment as intended.
You're right for all we know they could have been non-enchanted useless broomsticks that couldn't fly and the trio would have kind of died there.
But I think since its the "Room of Hidden Things", we would not expect ordinary objects (like a cleaning broomstick) to be put into that room. But you would most definitely have/expect a flying broomstick. A non-enchanted broomstick would be too much of an useless object to go and hide it in 'Room of Hidden Things'.
Oh! and you can identify a normal broomstick (no handles no polish) from a flying broomstick (polished, bristles are neat, has handles and markings). Since 1900s, all broomsticks were mass produced with polishing and a lot of tidying up [source: Quidditch through ages book]
And I think some things happen to conveniently be available at the right time just for the sake of moving the story forward. This is not specific to Harry Potter but I guess in general applicable to many stories/movies.
Of course, a broom would have to be enchanted in order to fly, however wizards have absolutely no use for ordinary, non-enchanted brooms. No self-respecting wizard would clean their house using "muggle methods" (for example Severus Snape considers that a particularly cruel form of punishment in his detentions).
So it is safe to assume that any old broomstick you happen to stumble upon in the wizarding world can actually fly.