BF1 isn't very CPU demanding, but you forgot to talk about
i3 6100 bottlenecking R9 380X/960 level card in Assassin's Creed Syndicate, ARMA 3, Rome 2 and sub-30 fps dips all over Crysis 3. Now to upgrade that PC you have, you need to sell i3 6100 with a loss in resale value and buy an i7 7700K, when you could have just purchased i7 6700K in the first place and enjoyed 14 months of superior performance. Chances are 7700K will not overclock much better than 300mhz over the average 4.7Ghz overclock of the 6700K.
There is nothing wrong with a budget i3 6100 + GTX960 but constantly paint this system only from the positive side and ignore all the benchmarks where i3 6100 or GTX960 aren't performing that well.