That is generally what someone who accidentally bought a 7600K tells themselves...
Note just how well the i3-7100, i3-8100, and R3-1200 do in Battlefield 1 and Battlefield 5 CPU comparisons these days...(particularly in the
minimum FPS levels) Compare a 7600K to an 8700K in BF1 or BF5 when both are running at 4.7 GHz with a good GPU. If your theories are correct, their frame rates should be quite similar.
Fast forward to 6:17 in the video (below) to note the 7600K's fairly dismal minimum FPS...; fortunately, the 2200G/R3-2200 are not shown, as the results would be even lower.
View: https://www.youtube.com/watch?v=2NdkShPrAKM
You, of course, are encouraged to buy whatever you feel is adequate. I'd refrain from recommending such CPUs to others for gaming systems unless quite sure on your conclusions...
If your theories are correct, you might be able to find some good i5-7600K /i3-8150K pricing deals these days as everyone else on the planet 'mistakenly' dumps them...