TL;DR: 3070 is not overkill for AAA games ultra. Its overkill for competitive shooters at competitive settings. 3600 is good for the second case, but not necessarily for the first case.
If you get 3070 for 1080p, then you are targeting high refresh rate (>120 FPS). And, since 3070 is a very powerful card for today's games, you are going to run into CPU bottlenecks in many games (meaning, you may notice GPU at <90% utilized, which cuts the frames, obviously). So, you need a powerful CPU, definitely more powerful than a 3600. I have a 3600 running at 4.2 GHz all cores paired with 5700XT for 1080p 144 Hz. Even with this, I find games that I run into a GPU or CPU bottlenecks. e.g. CSGO runs at >300 FPS with CPU and GPU utilized at 30 to 60 percent at 1440x1080 res. SOTR ultra DX12 runs at 99% but is mostly below 130FPS. With minimums dipping down to 65. My freesync range is 70 to 144. So, you can imagine, the shit I have to go thru when the FPS is below 70. So, check what your monitor's freesync/gsync range is, its VERY important. And, how do I keep the minimum FPS above 70 - Get a better CPU. 3600 just doesnt cut it even in a 2018 game for high refresh rate gaming. Dont get me wrong, its an amazing processor, but good is defined as 60 to 75 Hz gaming in this case. Anything above it, needs more CPU, in my experience.
Like I keep saying in other threads, high refresh rate gaming needs a powerful GPU AND a powerful CPU. Getting only one of those is going to result into slight disappointment (as in my case). In my view, 60 FPS gaming is good, when your 1% lows are above 45. Similarly, 144 FPS gaming is good, when the 1% low is above, e.g. 90 FPS (Just examples brothers, everybody has a different view when it comes to 1% minimums). I got a 3600 because everybody kept saying its enough for 144 Hz gaming, and if you play any thing else than the competitive online shooters (APex, CSGO etc.), you need something more that that.
What games do you please BTW? At what settings are you targetting those?