A bottleneck iin general is not a bad thing and in reality every system has a bottleneck. Until the uprsing of SSDs the hard drive had become the biggest bottleneck. There will always be one component that is slowing down the rest.
Think of it this way, if everyone is driving 80mph and one guy is driving 79.5 mph (assuming there is no way to pass) then everyone gets slowed down to 79.5. Marginaly annoying but no big deal.
Now lets assume that someone is going 45, now everyone is slowed down to 45mph and it makes a huge deal.
For your specific example it completely depends on what is being stressed, the CPU or the GPU.
If the game uses 80% GPU and 20% CPU to run then the higher end the GPU the better.
If it is say 60% CPU and 40% GPU like on a CPU heavy game like BF1, then that i3 is going to choke and you will actually get the exact same frame rate with the 1080 vs say a 1060, thus the $400 difference is a huge waste of money.