Brains really do use "subsumption" (in the https://en.wikipedia.org/wiki/Subsumption_architecture sense) to accomplish various features; there are motor signals that some earlier-evolved part of the brain would be emitting if they were the only thing "online" in the brain, that are actively suppressed or "overridden" by another, later-evolved part of the brain, often a part that only "comes online" later in brain development. (Thus "early instincts" that disappear during development, like the infant diving reflex.) Often, these subsumed neural processes reappear when the region suppressing them is damaged, as in the normally-suppressed human lordosis reflex, or the normally-suppressed-after-infancy suckling reflex in most mammals.
There's no evidence that I know of that the limbic system and the cortex are in this sort of relationship; I'm just saying that this kind of relationship isn't unprecedented as a thing human brains do.
If such a relationship were to exist between the cortex and the limbic system, then both regions could be said to be "in charge" of cognition; sort of like a television tuner and a VCR can both be in charge of the image being displayed. One state machine (the TV; the cortex), passing input through to another state machine (the VCR; the limbic system) only in some subset of its states (the right "channel"; the right arousal state.)
It's true that in mammals (possessing a neocortex) the cortex takes over various processes traditionally performed by the limbic system. Complete removal of the cortex in rats demonstrates that behaviour can revert to entirely limbic control: https://www.ncbi.nlm.nih.gov/pubmed/564358
While the cortex can definitely be / become "in charge" of complex intelligent behaviours, it may still need the brain's phylogenically older machinery to bootstrap it.
Looks like a kind of "deep" architecture:
"It does this by decomposing the complete behavior into sub-behaviors. These sub-behaviors are organized into a hierarchy of layers. Each layer implements a particular level of behavioral competence, and higher levels are able to subsume lower levels (= integrate/combine lower levels to a more comprehensive whole) in order to create viable behavior. For example, a robot's lowest layer could be "avoid an object". The second layer would be "wander around", which runs beneath the third layer "explore the world". Because a robot must have the ability to "avoid objects" in order to "wander around" effectively, the subsumption architecture creates a system in which the higher layers utilize the lower-level competencies. "
One can imagine how backpropagation style training on "explore the world" or other high-level scenarios would result in formation of "avoid objects" kernels at the lower levels similar to how image recognition deep nets produce Gabor like kernels at the lower levels. We do have some theorems on optimality of such deep networks for image recognition and i wouldn't be surprised if similar optimality was present for behavioral deep networks. Also, it seems that like in case of image deep nets, the deep architecture for behavior naturally allows for transfer learning by reusing the lower layers too - like one would reuse the low/mid layers of image deep net, one would naturally reuse the lower "avoid objects" layers (and may be some more complex aggregate behaviors from "mid-levels") for other tasks.
What we really want is a robot or a car that can orient itself in the abscence of structured data and doesn't glitch out into the wall once it loses its objective. And even primitive animals are very good at that.