Can - on a very coarse level - the functional role of dendritic processing as a whole (at least one of possibly many functional roles it might play) be described as rewarding spatially coherent synaptic inputs when creating action potentials?
This would make sense, when the mapping of neurons to synapses was neighbourhood preserving (in the sense of topology): the efferent synapses of two neurons in close vicinity (in other parts of the brain) sit in close vicinity on the dendritic trees of their common target neurons.
Then it would be desirable, that when a group of $n$ neurons in close vicinity to each other (e.g. a nucleus) projects to a subtree of the dendritic tree (i.e. synapses in close vicinity) and those neurons are firing at the same time, this should evoke an action potential in the target neuron, but not, if $n$ synapses spread randomly over the dendritic tree are active at the same time. To achieve this could be the (or one) function of dendritic processing.
As I said: this is a very coarse level of description, and to be taken with some grains of salt.
(The whole question would break down if there is no such neighbourhood preserving mapping from neurons to synapses.)
I've read the following articles (but maybe not carefully enough to be able to pin them down to the short form above):
Stuart/Spruston, Dendritic integration: 60 years of progress
Poirazi et al, Pyramidal Neuron as Two-Layer Neural Network (this article comes closest to the spirit of my question)