290/290X released for much lower prices then their competition and forced Nvidia to drop prices. Win for AMD and Nvidia consumers.
980Ti was released at $550 to compete with the Fury X. If AMD had no card to compete with the 980Ti at the time, I think it's safe to say the 980Ti would have been much more expensive as we saw with the release of the Titan X (P) (I realize the Fury X dropped after the 980Ti but Nvidia had to have had some idea of the upcoming competition when it set the 980Ti price). Win for AMD and Nvidia consumers.
RX 480 releases at $200/$240 and the GTX follows soon after at $240. Would the 1060 have released at that price point with no 480 to compete with? Seems highly unlikely. Win for Nvidia and AMD consumers.
Strong competition is better for consumers because it keeps prices in check and causes each company to strive harder to win over consumers. What does that extra "striving" look like? More tech features, game bundles, software innovations, overclocking options, etc.
Nvidia also puts pressure on AMD and it is very likely the gtx 1060 would have launched at 250/300 with or without the rx480. This is because if you look at the pricing of the 1070, that was the only price it could have launched at while maintaining the value proposition of a 1060. A 300 and 350(founders) dollar 1060 doesn't make sense when the gtx 1070 is 38% faster. And considering midrange has always had the highest price to performance, a 300 and 350FE would do poorly in reviews and thus poorly in sales.
Looking at all factors, its Nvidia striking first and pricing the gtx 1070 at 380/450 that made the rx 480 pricing as it is. Finfet is more expensive than 28nm ever was and yet for the first time, AMD priced their cards for the die size, cheaper than the 3870 which was almost 9 years ago. The 7870 from AMD was smaller than polaris and had a less beefy power delivery system, yet it was priced at 350 dollars.
Look at AMD terrible pricing segmentation and you can see that 250 dollars is too low of a price to fit 6 products in it with 120 floor pricing for the rx 460. E.g rx 480, 470 and 460 and their different memory variants. What having such closely spaced products does is it causes cannibalization of sales and confusion around consumers. You want discrete pricing segments which maximizes potential profit. E.g the sales of one card doesn't mean the loss of another one.
I think AMD wanted to price these cards at 300 dollars, but with the gtx 1070 being 50% faster, that plan went out the window.
As a result of Nvidia brand prestige and the looming threat of the gtx 1060, AMD had to price their cards at 240. Particularly for marketing and review purposes. Any higher and polaris would have gotten a bad review because it would be conceding performance per dollar, per watt to the 1070 and a bad review on a new chip is the last thing AMD needs.