One of the benefits of the technique I presented is that it's actually easier to reach a working program quickly.

When you write in layers from the bottom up, you test each layer which is simpler than the whole program, and thus assure yourself minimal bugs (debugging usually takes more time than code-writing). When you write the next (higher) level, you rely on a tested lower level and have more confidence. Massive unit-testing along the way and you're set for a working, clean solution.