Your first point is not true. I have pointed out several canon facts that suggest multiple timelines. Mainly, the OoT-TWW connection, and FSA. And Aonuma's quote counts too, if not in the same sense as the games.
I don't like a lot multiple timeline theories because they have never been suggested by any canon fact, plus, they make are a complete joke, using them you can practically place the games in any order you desire.
You can place the games in any order you desire with single timelines too. There's no difference moving from single to multiple timelines. With either ones, you can make whatever order you desire by introducing your own assumptions. Both single and multiple timeline theories are equally susceptible to the introduction of assumptions.
The only way the split timeline theory differs from the single timeline theory is by the introduction of a single assumption: a timeline split during OoT, in which both timelines survive. This makes many connections between the games easier to explain, and each of the two timelines follow the same rules as a single timeline would follow. It's not like having split timelines leads to chaos and anarchy. There are still rules. There is only ONE split we know of, and each timeline has to conform to the same standards as a single timeline would conform to. So what exactly is the problem? You can't argue that split timelines can be abused, because single timelines can be abused in exactly the same way: by introducing too many unnecessary assumptions. The assumption of a single split in OoT is not unnecessary, since it explains a lot of things and is implied by canon facts and by creator quotes.