SUPPORT: There is no supported capability to do that with any "COMPANY_NAME" product, thanks.
CUSTOMER: FYI, in 2015, that’s absolutely TERRIBLE. None of the other premium providers game me a STRAIGHT NO.
1. Sometimes, when support made the wrong initial contact, all future correspondence will turn sour. Make the first impression count.
2. Having 'thanks' at the end of sentences seems casual/unprofessional to me, if not rude. Maybe something like "thank you for your message" as an opening line on that email might be better.
3. At least you should have offered alternatives, rather than leaving the customer empty-handed. If there are none, at least you could have said that "we are looking at/thinking about/working on/still gathering feedback from more customers/ to implement this feature in the near future. as soon as it's ready, we'll let you know."
4. I think most of your replies are too long. On the other hand, your initial reply almost looked like canned response.
5. Never vent out to your customers as support. You will never win. You have the final say on what features you will put to your products, but your customer has every right to express how they feel about your product/service. You have none. Don't take it personally.
disclaimer: I am writing based on experience