I'd expect a good increase in fps in a lot of games even with that cpu.
do you have before and after fps figures for some of the games?
could you monitor the cpu utilisation of each core and also the gpu utilisation % using msi afterburner with an overlay set up?
I think you're dramatically over-estimating the capabilities of this CPU.
In BF1 it struggles to maintain an average 30fps and drops to sub 20fps in maps like St. Quentin Scar in some spots.
Meanwhile a GTX950 is capable of running the game at 1080p medium at a solid 60fps.
He made the mistake of assuming his GPU was the problem when it was pointed out in another thread that in fact the A8-6600K was bottlenecking the GTX950 hard, let alone a GTX1060, but he went ahead and bought it anyway.
A GTX1060 will run the game at 1080p ultra 60fps but it needs to be fed by a strong CPU, an FX8320 and above or Ivybridge/Haswell i5 and above ideally to get full or close to full utilisation in many titles.
You're wasting your time advising him to monitor GPU usage, core usage, etc. This isn't a technical problem, it's an issue of pairing an ultra low end CPU with a high-end GPU.
The only way to alleviate pressure on the CPU is to run at ultra settings 1440p, or 1080p ultra with supersampling applied, but as the poster correctly pointed out above, that does not solve the problem of very low framerates, only allows you to run at better image quality settings while still having a crappy framerate overall.
If he upgrades to Skylake i3 or i5, the problem will resolve itself, though obviously better on the i5.
It's a very straight forward situation, there is no 'issue' or technical problem.
You can get entire A8 and A10 based machines on Ebay for £80, they are not, and never were, designed to be paired with high end GPU's - they're built to run games like World of Warcraft, CS: Go, MMO's, etc.