Intuition / Importance of intermediate supervision in deep learning
Unfortunately there is no mathematical proof whether or not the intermediate supervision improve the performance of the network. 

However stack hourglass article shows that according to ablation study: using more encoder – decoder units with intermediate supervision improve the performance – please have a look at the figure below.

In that case – the remaining network doesn't perform identity transformation (although there is a residual connection between the remaining networks).

My intuition is the every encoder – decoder serves as a PCA,  that keep the most dominant feature maps.  A series of encoder – decoder let the network reassess the feature maps until it get its most discriminate feature maps at the end.