I've been practising BDD for a few years now. For whatever reason I'll sometimes find myself coding without having first written a reason. You know what, I always find that I'm really not enjoying writing the code. The reason, I'm constantly having to guess about whether or not the code I'm writing is actually useful or not. Every time I write a new method signature I have to try and imagine the whole system that's involved for that feature and figure out where this little bit that I'm working on fits in. It's a lot of mental work compared to the alternative. Working outside in you never have to think about the big picture, that's where you started, all you have to do is keep drilling down into the detail until it works. There's no room for drift, if you're disciplined you can always do a minimal amount of work to get the job done. Thinking about code in this way, one little bit at a time is so relaxing. Get interrupted, that's fine, go off fix the urgent bug or whatever. When you return just your tests, see where you got to and pick up where you left off. Because you've externalised your thinking so far you don't need to carry it around in your head. You're back in flow in a couple of minutes.
tldr, BDD can make coding a far more relaxing experience whilst helping you focus on adding value, not waste.
Sure, testing does cover some of that but it is difficult to get 100% test coverage. And the 100% coverage is the liberating aspect.
When I hear people say "We have 80% test coverage" I just shake my head. What in the heck does that mean? It means that when I make changes to system, I can still break the behavior. And it is expensive to get 100% test coverage. In a startup, I agree, in many cases it might not be worth the investment.
With BDD, it is very easy to get 100% behavioral coverage. 100% coverage means that there is no way I can break the software (the behavioral aspect). And, using off the shelf DSLs, I can often write scenarios that require me to write 0 lines of "test code". So, I get that coverage for free (which is why it can be very useful for Startups).
Of course, if someone lays out a web page which somehow hides the submit button. Well... Then I guess other tools are needed...
tldr, BDD can make coding a far more relaxing experience whilst helping you focus on adding value, not waste.