The systems we think are simple are only so because we already possess the knowledge necessary to think abstractly. (Or somebody else does.) Now consider this too: our knowledge of cellular biology is infantile. Can we put the entire brain together without understanding its parts? I bet you we can't.
We have to have a model to start with. In this case I don't mean a computational model that simulates everything--just a mental model. A physiologic model. Something that can tell us xyz happens in response to foo or absense of bar. We've been building that for a while now, but we're nowhere near complete. Not even enough to "wing it".
Complex problems can be solved with adequate information. We, unfortunately, are at a loss for that. (At least as far as applications at this scale are concerned.)
I'll make an informed prediction though: you'll see simulated brains working after we've cured cancer and aging.
If by that you mean that science proceeds by first understanding systems in their entirety and then abstracting away the essential elements from that complexity then I can't agree. (Science education may do that but that's an entirely different matter).
Historically we've gained understanding of systems by creating simple models which capture their essential behavior and only later adding more complex effects. One good example is the dynamics of the solar system. The basic phenomenology of central force motion (ie. elliptical orbits) was understood long before N-body interactions were accounted for. I think you would find similar examples in biology. For instance the "rule" that DNA is transcribed to RNA was established long before exceptions like retroviruses were understood.
The challenge is and always has been to somehow "see" or intuit the fundamental behavior in a mass of confusing data then build testable models based on that intuition.
Until you've discovered how it works you won't know which features of the system are actually essential to its functionality and which are mere evolutionary artifacts which can be drastically simplified.
I think the problem will be solved, like other scientific problems have in the past. People will have ideas about what is essential and they will construct hypotheses and build and test models based on those ideas.
I think that arguing that the problem is too complex therefore there's no point in people having ideas until we can model everything is not a productive approach.