I understand where you are coming from. Coming from my belief system, the body is trivial in many ways, (or at least comes across as so to me from what i've read).
I also understand what you mean by our soul pervading our bodies. But I recall from Baha'i Writings things that say essentially that there is both a soul and a spirit. We believe only humans have souls, and humans also have a spirit. However, animals only have spirits. Essentially, the spirit is the personality of the being.
And in the next life, we will have no physical bodies, however we will be able to identify each other by our spirits (personality) in a non-physical form.
So to me, the body is essential in the creation of the soul and the development of the soul through experiences, but the soul and spirit then become completely independent and no longer connected to physicality.
I guess the body is just the vehicle?

Sorry if this is really confusing/disjointed! I should probably just go to sleep!