"Because no two aizome-dyed items end up looking exactly the same, the fabrics take on a solitary luster that the Japanese have appreciated for millennia."
Although it took about 5000 years for indigo dyeing to reach Japan, we now consider it a Japanese craft in the same vein as woodblock printing. And considering some of its main attributes, it's not hard to see why the Japanese took aizome to their hearts.
Because no two aizome-dyed items end up looking exactly the same, the fabrics take on a solitary luster that the Japanese have appreciated for millennia. Adding to this is the fact that indigo mellows with age (but doesn't fade), which gives it wabi-sabi like characteristics. Put briefly, as the fabrics age they obtain a rustic, imperfect beauty that is treasured in Japanese aesthetics. Something similar can be found in the ceramics used in the tea ceremony.
Another factor that have always appealed to Japanese artisans is being creative through simplicity, applying as few elements as possible. In this case only two colors - white and blue - are used in the dyeing process, yet the creativity to produce truly unique results through various techniques and styles with utmost perfection is astounding.
But perhaps the most Japanese aspect of all, or at the very least a fun fact, is the bubbles or foam that forms during fermentation, right as the dye is ready to be used - the indigo blossom, or ai no hana. As with cherry blossoms in spring, the Japanese cherish this transience of things, mono no aware. Now, indigo blossom is of course created through a human process rather than the flowing forces of nature, but the Japanese still have a sense unlike any other people to find meaning and beauty in everything.