At my previous firm in Buffalo, NY we were hired on occasion to design steel girder erection plans for bridges, and we always did an analysis considering the lateral stability of the girders for their self weight. We considered the stresses when the girder was lifted by the crane, and when it was set in place.
As for adding additional bracing or doing other things that may add a small amount of money to the job, our primary responsibility as structural engineers is to design safe structures. Economy is definitley a consideration, but it has to take a back seat to safety. Too many owners (and architects)don't care about this as they apply the thumb screws to get designs from structural engineers quicker and for less money, with the resulting structure as cheap as possible. I am writing this at 7:10 a.m. on Saturday to try to get another job out to meet an aggressive schedule. Again.