While you're right that the Barney's website is dogshit, I don't really understand your complaints about the LA store. As has been pointed out -- and seems to be alluded to in Barney's reply to you -- is that what the store chooses to buy and stock is a consequence of detailed market research and experience selling within the area. And simply because there's other stores locally selling the high end products you'd like to see doesn't mean that the products would sell well for Barney's -- maybe the market is already saturated, maybe those stores aren't really financially successful (or as successful as Barney's would like to be). Also, as you yourself point out, you've never had a bad customer experience, it's just that the SAs lack some undefinable abstract (atavistic?) clothing sense that you pine for and see in New York. How can that even be addressed? Maybe it's you, maybe it's the weather, maybe it's that the vibe is different from NYC.
I'm glad to hear that they're working on their obviously terrible website, but you presented your complaint as some sort of last-straw ultimatum, when it was really "I haven't had an outstanding customer service experience in your store, and I'm not totally sold on the brand selection." Is that really a calamity? And is it worth it for Barney's to cater to your needs? You might spend a fair bit, but I doubt you make the $40,000 impulse purchase of an Hermes fur that drives much of their business.
I also doubt that your letter is going to lead to fundamental changes in the way Barney's runs their business. While lots of people are stupid, what is true is that regardless of their response to you, Barney's is a large corporation where changes go through many levels of vetting and approval. But it is nice to see that they reached out personally to talk to you.
What is annoying though is that this whole letter has kind of a 'look at me, look at me!' sense to it. Is it really worth the fuss?