Not trying to be rude but do you know what you are talking about?
Yes, he does. More than probably 99% of the "supposedly expert" members on any forum you'd care to go to. And he's 100% correct that replacing the graphics card isn't what gives you an increase in frame rates, in most cases.
Replacing the graphics card allows you to increase graphical settings. GPU renders frames but rates are controlled by the capability and performance of the CPU. Now, it's totally possible to SEE an increase in frame rates sometimes by replacing the graphics card IF you are being bound by the GPU at a specific quality setting configuration, but what WILL NOT change is what the ACTUAL maximum frame rates CAN BE if you are using the same CPU.
You could put a 3080 ti in there and with the same CPU it's very unlikely that you're going to exceed the existing frame rates, ESPECIALLY at low quality settings. The lower you set the quality settings for just about any game, the MORE the CPU is in play. The higher the quality settings, the more the GPU is in play. So yes, in your scenario the most PROBABLE upgrade you could do without changing platforms (Meaning new CPU, motherboard and memory, to newer generation) would be to source and install a compatible Haswell i7 such as the 4790 or 4790k. Since you have a locked model CPU then overclocking is out of the question for all realistic intents and purposes. Upgrading to an i7 may offer some increase in performance but most especially for titles that are highly optimized for multithreaded performance.
For titles that are primarily single threaded, upgrading to the 4790 would only give you a slight bump in single core performance with it's 4Ghz turbo boost as compared to the 3.7 boost on your 4590, and the 4790k would offer a bit more respectable single core gain with it's 4.4Ghz max boost, giving it a total of a 700mhz boost over your 4590. Now, whether or not that is an upgrade WORTH doing in terms of performance versus cost will depend entirely on if you can find one, how much you can get it for and whether that even makes sense for you or not.
Personally, I'd say given the age of your system and your statement about being a competitive player, that a whole platform upgrade makes a lot more sense but it seems rather dubious to see a "competitive" player using hardware like an R9 270, or even an RX 480, and a platform with a CPU that is 7 years old.