I was one of those customers who did not care about the increase. I thought it was understandable. Having both streaming and delivery for the same price was too good to be true.
You may have made mistakes in the way you communicated the increase to your consumers, but that is nothing compared to the branding and marketing mistake you are making now.
I'm sure you will find that your letter, far from appeasing your customer base, is going to have the opposite effect.
The name Netflix is such a powerful, unique brand that it has become a verb. But besides misadventures in marketing, which customers care absolutely nothing for, (all we want is quality, convenience and value), why would your customers who would like to enjoy both services want have to deal with two separate sites, under two different names? The refusal to integrate both services under the Netflix brand is incomprehensible to us run of the mill humans; only marketing mutants can understand such absurd decisions. Why would we want to have two separate charges in our monthly credit card bill? As if people don't have enough saturation on the internet already. Why not leave both under the Netflix name and figure out a way to bill customers without inconveniencing us? Nobody needs yet another brand in this world.
I was one of the first users of Netflix and I evangelized about it to anyone who would listen. It pains me to deal with these issues after so many years of being a very happy customer.
The Grande Enchilada.