they arent weak, but you can get more performance for less money with intel in most scenarios. only 3 reasons to buy amd:
1 is the better multi thread performance for VMs, for rendering, etc
2 is that you want to give amd money so they can compete with intel which is better for the market on the long term
3 is that they arent affected as much by the recent security bugs with concurrent access which intel hasnt fully patched in the current generation.
if you buy a i7 7700k and an rx580 now, you can buy a second rx580 second hand soon, or buy a rx880 or gtx2260 in 3 years. in new dx12 games multi gpu or replacing gpu every 3 years will get you good scaling on performance, in old games without great multithreading, the single thread performance of intel will be better and the rx580 is more than good enough. that you can get marginal extra performance in some games with cheap amd cpu and expensive gpu now, doesnt mean its worth it over a period of 3-10 years.
if you buy an average cpu now, you will have to replace it in a couple years, instead of it lasting for 10 years like an i7 would, and the 1070 will need replacing only 1, maybe 2 years later than an rx580 or 1060 3gb, while it is 2x as expensive. the xx70 or xx80 cards with nvidia are never good in price/performance department, so to justify spending that amount of money on gpu, for me, i would need a 400 euro i7 as well.
i also wouldnt recommend buying a 4 core locked multiplier intel anymore even if its very cheap for the same reason, it wont last long enough. its just not the most economical choice to skimp on cpu, imo. you have good arguments though.