No objection (currently they look more like they are levitating than climbing IMO), but there are other things on which I'd rather the time that would be needed to code this was spent.
Something as simple as rotating a model 90 degrees really shouldn't take too long; we already have upside-down models (via "Dinnerbone" nametags on mobs). Then again, considering the rate at which updates are coming, I can see your point.
Nevertheless, I have Full Support for this suggestion. This would be a simple aesthetic change that would add a little touch to the gameplay.
I support this, but you are not only talking about coding the model, you have the hitbox rotation, Flipping a model upside down should be pretty trivial, you don't do anything to the hitbox. Rotating the spider hitbox 90 could be a huge mess. If you rotate the hitbox, does it spin on the center? Would that cause the spider to "fall" attempting to climb, since its feet would no longer be against the wall? If you do the rotation "feet against the wall", does that mean a spider could pop into a barrier that then allows it to climb past certain partial blocks intended to act as a barrier? What are some other unintended consequences of rotating a hitbox?
Take a more or less square book, pretend it is a "spider", see if you can come up with some simple rules for how to rotate the book around obstacles without introducing some messy hitbox collision bugs. I can't imagine anyone at Mojang would want to touch it. As it is, a spider "works" because it is a 2x1x2 entity that sees a ladder on every verticle surface, and so that is exactly how it behaves.