You can still cut costs in your build by using an A520 mainboard and a cheaper case (this CPU + GPU combo doesn’t care much about good airflow), so you can get below $600 for sure. As you say though, you still need a mouse and keyboard. If we count a display it’s only fair that we’d count a TV in addition to the console as well. Then you need an OS as you say, but here in Europe you can legally acquire a used Windows OEM license for dirt cheap (like 5 bucks), or you could always run a Linux distro for free.
And of course when you buy PC parts you either have to build the PC yourself (which is quite easy these days though) or pay someone to build it for you (or you know a good friend who does it for free).
You didn’t mention optimization but it’s what many people bring up as a pro for consoles, where they think spec for spec console hardware performs better because of it. This isn’t the case though, especially with the last two console generations.
I’m sure we could both list hundreds of pros and cons for each platform, but what it comes down to for me is value. Sure, a PC might cost more upfront (even though as I said it can turn around after a few years). But with a PC you get a system that’s not locked down. You have access to a huge library of games, the backwards compatibility is insanely good and you can potentially get more value out of every game purchase because of support for mods for example. And of course you can do a lot more things than just gaming.
I don’t think console gaming is dead in any way, but I don’t think the reason keeping consoles alive is value.