Neuroimaging recordings during resting state (but also in tasks) reveal that brain-wide functional connectivity networks are highly dynamic, undergoing a structured flow of stochastic-like reconfiguration, with events of transient stabilization of connectivity, intertwined with "leaps" with high and fast variability. Markers of dynamic functional connectivity are increasingly being used as biomarkers of various pathologies and cognitive performance. Here we ask whether there should be some deep reason for Functional Connectivity to be as dynamic as it is observed to be. Functional Connectivity indeed is supposed to reflect inter-areal information exchange which could also be optimized by designing a specific stable functional connectivity network that would be very efficient in dispatching information. However, the rule of the game may change if we suppose that generating a functional connectivity link for a certain time has some cost (e.g. of metabolic nature). In this case, efficient static networks may be very costly requiring a large number of unused links, while randomization of links could provide a compromise allowing suboptimal but still efficient information diffusion at a smaller overall cost over time. Considering the cases of omniscient information spreaders, random information diffusion and info-diffusion driven network reconfiguration, we explore and identify regimes in which the emergence of restlessly dynamic Functional Connectivity could be seen as the byproduct of simultaneously optimizing easiness of communication and the resources needed to achieve it. Finally, we also compare the results of our theoretical models with observations of switching statistics in empirical fMRI resting state data.