Spine's a bit confusing for a new user this way.
Animators expect it to look like it's supposed to look in Spine Editor. But Spine editor autoresets the skeleton whenever you play an animation or switch, while the runtime doesn't assume that this is what you want.
Using the logic of "key it if you want to be sure that's how it starts", a user would (and I've seen people do) key every scale, rotation, translation of every bone and every slot attachment and mesh vertices and pretty much the whole setup pose at the beginning of every animation, just to be sure that if any of them were changed by other animations, that the animation would still look like the way it was animated in Spine editor.
I've seen a good number of people do this, and it's terrible to work with in the editor with all the extra timelines, and performance scales horribly at runtime.
(Actually, their reasons for doing this isn't just for resetting the skeleton.
Some people do this so it's simple to copy exact poses from one point in time to another, or between animations.)
But you're right. If it's just the draw order, I guess one extra timeline isn't a problem on either side.
But it is one extra thing to add to who knows how many animations. It's probably not an unsurmountable problem in that sense.
If the behavior you need is for the skeleton to use the setup pose draworder unless otherwise specified, the method to reset the draworder will do the job without having to make sure stuff is keyed in Spine editor.