2060 is the true successor to 1060 since it's performance is similar to 1080. (1060 is equal to 980).
In terms of chip size, power draw and price, the 2060 doesn't bear much resemblance to a typical "x60" card. The chip it shares with the 2070 is actually larger than those used for the 970/980 and 1070/1080. And as previously pointed out, the 1660 cards fit that role more closely, and even they use a chip nearly as large as what the 1070 and 1080 had used in the previous generation...
GTX 960 = 227 mm2 - 120 watts - $200
GTX 1060 = 200 mm2 - 120 watts - $200/$250
GTX 1660/SUPER/Ti = 284 mm2 - 120/125 watts - $220/$230/$280
GTX 970 = 398 mm2 - 145 watts - $330
GTX 1070 = 314 mm2 - 150 watts - $380
GTX 2060 = 445 mm2 - 160 watts - $350
GTX 3060 = 276 mm2 - 170 watts - $330
GTX 3060 Ti = 392 mm2 - 200 watts - $400
Now, the 3060 uses a chip more comparable in size to the one used for the 1660 cards (and different from the much larger one the 3060 Ti shares with the 3070), though even the 1660 cards used an atypically large chip for an "x60" card, and there was a process shrink this generation. But the TDP actually increases to 170 watts to get the most out of that silicon, well above what is typically seen for an "x60" card, and near the level of even some "x80" cards from the past.
What ultimately determines a card's successor is what price bracket it is targeting though. Those in the market for a $200-$250 card are not likely to spend $350 just to follow some completely arbitrary model numbering scheme that the manufacturer changes on a whim. AMD similarly shifted around model numbers from RX 550/560/570/580 to RX 5500/5600/5700 last generation. The model numbers might follow a similar trend, but that doesn't mean the $400 RX 5700 XT is in any way a successor to the $170 RX 570. So the only logical way to compare cards from one generation to the next is to look at how much performance you get at a similar price level. The 1060 is targeting an entirely different price bracket from the 2060 and 3060, so it doesn't make much sense to compare performance gains to that card.
So, to go by a somewhat more logical comparison, using MSRPs along with techpowerup's reference 3060 12GB review numbers at 1440p (and the 2060 review numbers for the 970)...
970 -> 1070 = ~60% more performance @ 15% higher price = ~ 39% better performance per dollar
1070 -> 2060 = ~19% more performance @ ~8% lower price = ~29% better performance per dollar
2060 -> 3060 = ~21% more performance @ ~6% lower price = ~28% better performance per dollar
...and...
2060 -> 3060 Ti = ~58% more performance @ ~14% higher price = 38% better performance per dollar
So, the improvements in value for the money at launch of the generation are almost exactly the same between this generation and the last for the 3060 and the 2060. The 1070 offered a bit more of an improvement in terms of raw rasterized performance for the money, as did the 3060 Ti, though at somewhat higher prices (ignoring current availability issues). If we consider the time between each generation though, the 1070 came out around 21 months after the 970, the 2060 around 31 months after the 1070, and the 3060 Ti and 3060 around 23 and 25 months after the 2060. That means the 1070 provided an improvement in performance per dollar of about 22% per year over its predecessor, while the 2060 only improved that by around 11% per year, the 3060 by around 13% per year, and the 3060 Ti by around 20% per year. So actually, the 2060 provided the least improvement over time of these generations, with the 3060 being slightly better, but still well below the gains seen by the 1070 and 3060 Ti.
The 2060 did add raytracing acceleration, though it's questionable how useful it will be on hardware with its capabilities. Especially since it has relatively low VRAM compared to other recent cards in this price range, and at least CyberPunk has already proven to be too much for raytracing on the 2060's 6GB, seeing a disproportionately large performance hit and only getting around half the frame rates of the 8GB 2060 SUPER when enabled, when one would normally expect it to perform within about 15% of that card. The 3060 12GB again does better here, though I can't help but think that designing it for 8GB could have provided a better balance between price and performance (again, ignoring the current market). There are rumors of a 6GB 3060 as well, though it will also likely suffer from a VRAM deficiency when enabling RT in Cyberpunk and other demanding future games, though perhaps not quite as bad when installed in a PCIe 4.0 capable system. If they don't cut it down in other ways it might offer better value for games not utilizing RT though, and could possibly even slip down near the 1660 TI's launch price, allowing it to compare a bit more favorably with that card.