The structural engineer's job is to make sure the building stays up, not only in normal conditions, but through a large wind storm or hurricane, through a heavy snowfall and through a large earthquake. How much they have to withstand is dictated by the building code, which has some tend to be conservative in big cities (ie requiring the building withstand worse weather than it is likely to see), and weak in lesser populated areas.  For the most part this involves adding big structural beams to the house, sizing them properly and specifying shear panels, which are simply walls covered in plywood and nailed a specific way.  Having a strong building is a good thing, but clearly there is some point of diminishing returns.  To further complicate things, the structural engineer will usually over engineer the house somewhat, and then the builder will sometimes do the same, because each uses the specification they're given as a minimum standard.

While there may have been a day when architects could do structural engineering calculations themselves, but it appears that no one does that now.  A good architect is at least aware of the structural implications of their design, and hopefully will avoid situation that require a lot of big beams.   In general this involves being aware of which walls are load bearing any making any second story load bearing walls line up their counterpart of the first floor, and avoiding unnecessary cantilevering.  Even if one is careful to avoid situations that involve large beams, they can creep in, because until you actually accounted for every aspect of the structure you won't know what structure you need. In our view this separation of function is a really bad idea, because you don't find out what kind of beams you need until you're really far down the path (and unfortunately, structural engineers are expensive, so you don't want to feed them any designs that aren't at least very close to what you want).

We got two surprises from the structural engineer: first that using the existing foundation stem walls was going to take a lot of concrete (an issue we wasted much design dollars on), and that the roof as designed needed support to take the required snow load (25lbs/sf).  The concrete issue wasn't really all that much of a surprise, since we all knew that turning a four foot wall into an eight foot wall was going to be hard, and based on Bob's limited remodeling experience, working around existing stuff is always way harder, slower and more costly than you can imagine.

The roof issue was more surprising, because the force of a roof is mostly outward, not downward, and as a result most of the downward force of a roof is carried on the exterior walls.  With this downward force comes an outward force, first solved in the 1100's by added buttresses to the outside of the building (check out any old cathedral). These days we use cross braces to pull the two walls together: for example in a truss roof the bottom board of the trusses performs this function.  Unfortunately the bottom of the roof is also the "third" floor, and so has a hole for the stairway in it.  Yet, it would still seem that the plywood flooring, would act as a one piece membrane and would compensate for this hole, but it is beyond our skill to calculate this. So we have bracing up at the peak of he roof to hold the roof up so that its weight is carried more in the center, and therefore eliminating the outward force.

The only conclusion we can think of is to have the structural engineer give plan a cursory glance and suggest where beams are likely to be needed.  And of course, try to find an engineer who knows how to think "green".