I really love this idea in theory, and I believe that for some system, specially mature ones, it may work well. I see good documentation as a super power; it empowers readers and motivate people to understand more about the system without being caught in the weeds of reading the source.
The source has baggages, and the intent of every single function calls is not always evident. Writing documentation up-front can help direct the source, but this is a tug-of-war environment. Each affect the other in its own ways.
And for that reason, documentation driven development can be a real drag. You start writing documentation with the best intentions, everything works great for this first release. But 2 months down the road you need to modify something and it has a ripple effect on many of the things you documented. It's a non-negligible cost.
I've been working on this open-source tool(https://github.com/pier-oliviert/sequencer) and I've spent a lot of time on the documentation. And what I described above happened. I wanted to make a not-too-big change, and it required me to rewrite 30% of the documentation. I still love the documentation aspect of it, but it definitively has a higher cost than tests, in my experience.