Well first off, Nintendo comfirmed it. You're right though, when saying there are good arguments against the split timeline. Truedge2097 on YouTube makes a wonderful arguement against the split timeline.
That said, you were wrong when you said there isn't any logical sense to the split timeline. Now before any Linearists try to stone me, I just want to remind you that all the timeline theories are completed speculatory.
In denfense of the split timeline, here it is. Since this deals with Ocarina of Time's multiple endings/lack of them, I won't bore you with talking about other games.
First off, when Zelda sends Link back, she says (something along the lines of) "the road between times is closed". This obviously means that Link can no longer travel though time. This could be translated that two alternate times have been created. Present from past although having the same history. Thus assisting my defense of the split timeline. Also, though not canonical, is the fact that it is much, MUCH more difficult to make a timeline with the linear timeline. Now I don't want to sound lazy or anything, but it is true (but that depends on your perspective I guess).
You mentioned that the split timeline is impossible because Zelda keeps the Ocarina of Time. Many Linearist have used this example against the split timeline. However this would result in a loop, but this would mean there is no timeline. Obviously that isn't the goal. The other interpretation is that the linear timeline is the child timeline. And that nothing happens after the adult ending. This is very possible and I somewhat agree. As for the Ocarina of Time staying with Zelda, remember that it is what we do in the past that affects what happens in the future, not the other way around (by the way, that was a dirrect quote from the YouTube theorist Lancun).
I really hope this makes sense to you.