And we're supposed to believe this "just happens?" Nah. There is genius behind this.
Although I WOULD be willing to sacrifice a few billion samples ...
I think there are. But we get fascinated by the fact that the variations from one branch to another are so slight.
My conjecture is that the original "seed" which grows to form the snowflake contains imperfections with six-fold symmetry and it is these imperfections that dictate the particular pattern of the branches. As the branches grow, additional imperfections occur but they have less and less impact on the pattern as the growth proceeds.
Our appreciation for snowflakes is much like how we see identical twins. The similarities between the twins is so striking and so unexpected for those of us who seldom see twins that we are amazed by the similarities. Those who are around twins eventually recognize the differences and the amazement lessens.
The "seed" of the snowflake consists of so many billions of molecules that the number of ways in which the molecules can fail to line up properly is as close to infinite as any natural process gets. There are enough variations to believe that nobody will ever see two identical snowflakes.