Why is it not the case, though?
I mean you have the seal placed on the sacred realm (courtesy of the Master Sword), we have Ganon able to operate through people and such from beyond the Sacred Realm (Aganhim), the often-referred-to sacrificing of Link to revive Ganon which is a very possible reason he keeps coming back (and why those Links are never heard from again)... I find it'd be a lot stranger for the game to be referencing an extremely similar and yet completely different sealing of the sacred realm and the triforce which Ganon was gunning for than it being the same one loosely strung together later to make it fit.
Though in the same way it'd be a nice slice of headache trying to fit it into the adult timeline there just doesn't seem to be anything to support it really being in the child timeline either. Unless I'm missing something glaringly obvious (which I've been known to do, to be fair).
Three words: The Wind Waker. Like I said, TWW crushed any chance of OoT being ALttP's backstory. TWW is confirmed to take place after OoT on the Adult Timeline, with no games in between. There's no room for ALttP at all. And even if TWW didn't exist, OoT still couldn't represent the Imprisoning/Seal War. Here's why, straight from Zelda Wiki:
1. It is said that the King of Hyrule commanded the Seven Sages to seal the Golden Land in the legends of the Imprisoning War. Even though it is never stated in the game, he is presumed dead, and the noncanonical manga states that the King indeed died in Ocarina of Time following Ganondorf’s assault on Hyrule Castle.
3. The story of the Imprisoning War states that there was no Hero found who could wield the Master Sword, yet Link obviously did discover the sword and wielded it in Ocarina of Time.
4. The Seven Sages are of all different races in Ocarina of Time despite that in A Link to the Past their descendants, the Seven Maidens all appear to be humanoid.
5. Ganondorf is sealed in the Sacred Realm with only one piece of the Triforce in Ocarina of Time. In the backstory for A Link to the Past, he steals all three pieces together and makes his wish on the united Triforce.
6. The Knights of Hyrule are not nearly as prominent in Ocarina of Time as they are in the Imprisoning War story. Only one knight is seen in a back alley, and though his dialogue indicates he was killed by Ganon, the battle waged by the Knights to protect the Sages does not appear in Ocarina of Time.
7. Ganon could not figure out how to return to the Light World after the seal was cast. Two sequels to Ocarina of Time, The Wind Waker and Twilight Princess both feature Ganon's return and death.
And there
is evidence that supports a Child Timeline placement of ALttP. Looking at the status of the Master Sword throughout the games, you'll find that ALttP fits perfectly after TP in the Child Timeline. The Skyward Sword first becomes the Master Sword in SS, which predates OoT. Then, in OoT, we see the Master Sword in the Temple of Time. In TP, it's located in the ruins of the Temple of Time, which have since become overrun by forests. The only other game that features a canon Master Sword is TWW, which takes place on the Adult Timeline. ALttP can't come between OoT and TWW, and it can't come after TWW either, because the Master Sword is stuck in Ganondorf's stone body deep beneath the Great Sea, hidden forever with old Hyrule. So the only place ALttP can go is in the Child Timeline, sometime after TP, where it fits very well. The Temple of Time was nothing but ruins in TP, so it would make sense that by the time of ALttP, the place was completely overrun by forests, explaining the Master Sword's location in the Lost Woods. It's obvious that that's the connection that Nintendo was trying to make when they made TP.