There are already several questions about the intuitive meaning of Noether's theorem, e.g. this & this Phys.SE posts (with not very satisfactory answers to me so far). Therefore, this time let's go in the other direction.
Is there some deep topological/geometrical explanation/reason for Noether's theorems?
To give an example, what I'm looking for is a reason like "the boundary of a boundary is zero" for the Bianchi identities.
Noether's second theorem (the one for infinite-dimensional groups) yields "generalized Bianchi identities" and thus I suspect there could be some similar deep reason?!