If AMD releases a RX 590 with a sub-$300 price tag, AMD could possibly have a winner on its hands and potentially steal some of Nvidia's GTX 1060 market share.
The problem isn't stealing the GTX 1060's market share, but competing with Nvidia's next generation of hardware. The 1060 is well over two years old at this point, and is already long overdue for a successor, which will likely be coming within the next couple months or so. If the RX 590 only offers around 10% better performance than an RX 580, then chances are good that it's not going to outperform the competition's next sub-$300 graphics card. And while a process shrink of this existing architecture from 14 to 12nm may help efficiency slightly at a given performance level, Nvidia are also moving to 12nm, so no gains will be made against the competition there, unless Nvidia simply re-badges existing Pascal cards for their new mid-range lineup. Even if they simply called a 1070 a 2060 and tossed a $300 price tag on it, it would still likely offer better efficiency and significantly more performance than what is seen here though.
Had a 12nm refresh been launched this spring, around 2 years after the RX 480, it would have been a bit underwhelming, though it would have at least given AMD the mid-range performance crown for a little while. It's likely that they didn't go that route due to cryptocurrency mining severely messing up the market at the time though. By this point however, AMD has been talking about 7nm GPUs being on the Horizon, and there had been rumors that they might be available in early 2019, but with a refreshed collection of 12nm GPUs likely coming out this fall, it means that 7nm mid-range parts might be farther away, and probably not within the first half of 2019. The RX 480 was great when it launched for $200-$240 in the first half of 2016. Two and a half years later, a heavily-overclocked RX 480 is not going to be all that impressive though.