We actually haven't demonstrated that many functions. It is a mistaken belief we have, mostly driven by presuppositions. We have shown associations, but we haven't proven them, as such. If you assign a mechanistic primacy to brain activity, then you could conclude that is where those functions reside, but that is essentially a circular argument.
Measured Brain Activity has not been demonstrated to correlate very well with consciousness though. They did studies recently in Australia, in which EEGs and fMRI was done on people under muscle relaxation, but receiving no Anaesthesia. So they were awake, but couldn't move (except for isolated forearm technique), with full recall. Yet, the EEGs and so, showed what would be the equivalent of someone under deep sedation or Anaesthesia, as we understood it (delta waves and sleep spindles, etc.). Likewise, studies utilising meditation have shown marked fMRI changes, which should indicate decreased activity, while subjects subjectively experience enhanced sensation. There are even those studies trying to correlate decision-making with brain activity (that controversially has occasionally concluded activity precedes conscious awareness, and thus concluded decisions were 'made' after the brain already started doing the thing). These have also only shown tenuous connections as such.
That is the point of this 'emergent property' theory of Consciousness. We can't demonstrate where it resides, or how it works, but we conclude it must be in the brain somehow on a priori grounds - and therefore label it an emergent phenomenon.
What we have shown is areas of the brain are associated with motoric function (the parietal homunculus for instance), or language and writing (Broca's area and Exne's area), language (Wernicke's area), emotion (Lymbic system), etc. When damaged, those functions are gone - but the brain is very plastic, so other areas can often take over some functionality. Sometimes, different systems even use different areas (Chinese logograms and Western Alphabets use different parts of the brain, for instance, or primary and second languages). Rational function has not been demonstrated to lie somewhere, only the methodology of its application - damage an area, and the brain will start making strange associations or such, but the principles underlying have not altered. We can see personality change in brain damage, but more associated with emotional disturbance or absences - not change in function, so much as deficiencies in coping or impulse control.
Further, a lot that is popularly thought 'settled' certainly isn't. We know precious little about how the brain really works. Even something as simple as involuntary breathing, in which we know the full neural pathway, the carotid and PCO2 intra-cerebral triggers; we can't actually explain properly how it works. It is fancy hypothesis and guesswork. A good example is Memory that you mentioned in the OP. We actually don't know how they are stored, just assume they are. Some hypothesise that the act of remembering creates them, others that it is stored in the hippocampus - though new theories rather suggest a more diffuse frontal cortex role for storage. The old idea of 'short' and 'long-term' memory also seem mistaken, as perhaps it is a functional divide. There has been a recent massive overhaul here. Sufficed to say, we know much less than popularly assumed.
So arguing that the soul is superfluous is really putting the cart before the horses. It is assuming the truth of a certain materialist hypothesis, that certainly has a lot of scientific evidence that doesn't support it, too. You can always square the circle by weasel terms like Emergent Property or a good old fashioned Petitio Principii, but it has by no means been demonstrated. So such an argument certainly holds little water, and amounts to a Science of the Gaps, assuming we will be able to support it later or placing our piecemeal and contradictory knowledge in a framework built around it. The idea itself, that we have significantly demonstrated the mental functions dependant solely on the material brain, is flawed.
Besides, the Dualism you suggest is a much later idea. Descartes created an I and a mechanistic body. Christianity with its Body, Soul and Spirit seems to assume all three (or 2?) must be present - hence Paul's dead in Christ, or the OT dead and living Nephesh and Ruach. It is not separable things in practice, though we do so in theory, so the radio or driven car are very poor analogies. Hence Christianity teaches that we shall receive glorified bodies at the Parousia.
I don't expect the soul or spirit to be markedly distinct from the body so closely associated with it, and neither does my religion traditionally teach this. That that body acts in conjunction with the soul, any religious person agrees with, so to see material factors associated with it, is to be expected. To assume only the material operative, is just that - an assumption, which requires excusing significant phenomena, like consciousness, and erecting hypotheses like its emergent nature or applying quantum probability, that is going far beyond what actual empiric evidence we have.
Traditionally the soul and spirit are said to exist. I see no reason to conclude this a worse explanation than the fanciful house of cards built by materialism, if you actually know upon what they base it. If anything, as it maintains our ability to Reason, while materialism inevitably does not (relegating it to determinism or non-veridical evolutionary differentiation), the Soul/Spirit hypothesis at least doesn't invalidate the reasoning used to reach it. So the Soul/Spirit maintains logical coherence and validity, while the Materialist Brain cannot conclude its arguments to be valid, and in fact undercuts it. To me, Reason seems my primary means of reality testing, so the one telling me my Reason is necessarily invalid, certainly cannot be supported as well as the other.
