I too have experienced this as a company grows, but I do wonder if it's inevitable. Sure you can't have a single person trust model anymore - but you can have a distributed trust model, or a scaled trust model.
One thing that worked really well at a big company I know was to raise the approval limit - things under a certain amount simple go through without the need for approval - this allows managers ( and managers of managers ) to focus on the bigger items, and reduces friction.
Then I would have managed to avoid the touch screen stupidity entirely.