It does not have to be. The English language has a process where phrases become hyphenated compounds which then become single words. It's permissible to be partway along that path, and for people to disagree where something is on that path.
Pick any point in the past few centuries, and there's going to be something, possibly nowadays always a single word, but not necessarily so even now, that was in a state of flux at the time. The same goes for today.
“Old growth forest” is incorrect in any formulation of English grammar that I'm familiar with. It's not about fixed phrases. It's about using an adjective+noun pair (in this case, old+growth) as an adjective modifying another noun (in this case, forest). This is a general rule that applies across the board, not an isolated phrase example.
The poster was correct in asking what a “growth forest” is, because without the hyphen, the phrase parses as an adjective (old) modifying a compound noun.
Hyphenation is useful in phrasal adjectives, like "heavy-metal shield" (to distinguish it from a shield that is of metal and is heavy, but is not or a for example Pb) or in something like "four-day trips" (the trips last four days; they are not necessarily four in number).
I like it too, and you're talking to someone who has been trying, mostly in vain, to teach his kids the difference between "I wish I was there" and "I wish I were there", or how you can get eggs from a coop or a coöp, and they're different things, but eventually the hyphenation dies out and the phrase remains.
Mandarin written in pinyin comes to mind as another example. Do you discount that because pinyin is not the primary writing system used for that language?
It means a mature tree in an old-growth forest. Trees that grow in the dense shade of other trees grow slower, and their growth rings are much closer together. The result is that a tree takes a lot longer to grow but it's stronger and harder than the same species grown in the sunlight.
The reason for the distinction is that most of the old growth forests have been clear-cut and the lumber available today is fast-growth farmed lumber. If you compare a 2x4 at Lowe's with a 2x4 out of a 150-year-old house, you'll see that the wood itself is very different even though the species might be the same. The tree the new 2x4 came from was fairly young, while the tree the 150-year-old 2x4 came from was probably centuries old.
Old growth trees are trees or forests that are centuries old and not recently cultures.