I am not sure the one-story versus two-story comparison is so simple. One example is foundation -- you would increase footing/foundation/masonry costs quite a bit if you tried to put the same amount of square footage on one floor instead of split over two. Same goes for roofing, and crawl/attic insulation.
I know when we started dissecting costs, there are some that scale with square footage (like flooring, drywall, siding, trim) regardless of the number of floors, and others that scale with footprint on the ground (like roofing, insulation, masonry, etc). Minimizing footprint for a given square footage, as you would do in a multi-floor, will make those costs a smaller fraction of the overall project. It's always a balance regardless of the number of floors.
As far as fitting stuff in, a good designer/architect can do it while being smart about square footage and not bumping the footprint. If you can take the time to do it the right way, it's a complex puzzle to make it all fit together. Otherwise, if you do it the easy way you may end up increasing overall square footage to accommodate interior changes, or with less-optimal layouts.
Stairs certainly eat up square footage, but there are several stair configurations that minimize the problem. For example, an L staircase with winders will put the upper section high enough that you can use the room underneath (wasting only about 20-24 sq.ft). Split level homes cram the stairs into common areas. And homes that mix one-story and two-story sections often integrate the stairs into transitional areas where they have minimal impact.
We started our design working with architects (my sister-in-law and her husband) and together we came up with a very good floor plan that met all our goals and packed a lot of living space together in an efficient manner. Then we took that floor plan and basic 3D massing to our builder and his designer, and got the outside styling done. To me, that is the best way do design a home. I see other designs where people start with the outside or the styling, and then come up with the floor plan, and it looks haphazard to me.
The other important thing is to think about what rooms matter and how they work together. In our first home we had a formal dining area that only got used 1-2 times a year (holidays with company) and a very nice looking front foyer that was dysfunctional as an entryway for day to day use. Both wasted spaces that were clearly designed for guests and not everyday inhabitants. Laundry room was on the first floor as you came in from the garage, and completely inconvenient to actually doing laundry. First floor bathroom was off the foyer and conspicuous with no privacy.
Our new home deletes the separate formal dining area in favor of an enlarged dining nook in the kitchen, and it ditches the front foyer in favor of a very functional mudroom (with hooks, benches, cubbies) that is a "hub" between the garage, front door, kitchen, backdoor, and downstairs hall. The laundry room is now on the 2nd floor in a central location near where we actually need to process laundry, and the first floor bathroom is out of sight of all downstairs gathering areas. We have accommodated holiday guests just fine without a formal dining room, and nobody seems disappointed when they come in the front door and there's no dedicated foyer there for show. Combined, that was a good chunk of square footage that got allocated to more important rooms.
Overall, I think it's good to have constraints in a project like cost, views, footprints, exposures, and lifestyle requirements. They box you in and direct the design to the point where it starts to come together on its own. In the absence of stuff like that, house design can wander in some crazy directions and becomes haphazard.