There are two sides to the argument, one of which is present for some people but not others, the FPS per £ spent, or just out and out value for money.
Logic would state that if you are running, lets say a 3570K, with 16GB RAM, and a GTX 970 and you want to upgrade for better FPS, changing the CPU/Motherboard/RAM is not going to offer much in terms or bang for your buck, and not really improve the FPS output from your system. The sensible option would be a newer, faster Graphics card e.g. GTX 1070, and possibly swapping out to a 3770/3770K, netting you a much greater level of FPS for similar monies spent to the CPU/Motherboard/RAM.
If you don't care about how much you spend, and have an unrestricted budget, then yes upgrading it all is going to give you some improvements over the aforementioned option, but the level of diminishing returns for the money spent will be incredibly noticeable. These videos help highly just how good old hardware still is, and how a lot of it can keep up with modern GPU's for the most part at 1440p/4k, but there will always be exceptions, and those will get bigger over time, but the value argument about how much you are paying to have 5/10/15/20/25/30 extra FPS is what really matters to the majority.
Until the likes of the equivalent of the GTX 1060, can bottleneck an older i7, and peg the frame rates to below 60, or with severe stuttering then then, don't spend the money on the CPU etc, spend it on games, spend it on a larger SSD, spend it on taking your wife out, or just put it away for a rainy day when you need a new CPU.