Nope.
It's a huge rip off, and you could easily build something better for less money yourself.
On top of that, those pre-built things tend to cut corners wherever they can. They might have a great GPU, CPU, and some nice storage options, but will often have a sub par PSU, cheap RAM, inadequate cooling, and a Mobo that can barely handle what has been shoved onto it.
There are a few simple things to know when building a PC.
Plan around your Mobo, and get an ATX sized board. There are smaller Mini-atx boards that might seem like a good deal to someone new to building, but those are for making minimalist PCs and workstations. They are too small to build something that is primarily for gaming and even if you can manage it, heat will be an issue.
You don't need a $500 mobo with multiple PCIe slots if you're only using one GPU, even if it's a dual GPU card. Don't waste your money. Just make sure you've got slots for decent Ram, enough USB 2.0 and 3.0 ports to fit your needs, a PCIe, and the proper slot for the model of CPU you want to use. Bluetooth is also very nice to have for a gaming machine.
You'll need to get the kind of CPU slot that works with the brand and type of CPU you want to use. You'll also need to be aware of what type and frequency of Ram you'll need to buy. Make sure it has enough connections and features you want.
Do not cheap out on your power supply or cooling. You don't necessarily need to go water cooled either. Most gaming systems, particularly ones running a single card with a decent CPU will remain at perfectly reasonable temperatures with just a heat sink and air cooling.
Also, to reply to the question of whether buying a PS4 Pro will be more economical.
No. It won't. There's really no situation where buying a console over a PC is going to be more economical. A decent PC will also more than likely last longer. There will be yet another generation of consoles within a few years, and games for a new console won't work on the old hardware.
With a PC, all you'll likely have to do is lower the settings a little for quite a while into the future. I invested in a high end GPU back in 2012, more than five years ago, and I can still run 99% of PC games at max settings at 1080p.
Even when I do need to dial things back, I can usually get away with knocking a shadows option down to high or medium and still keep everything else at the highest settings.
A PC might be a bigger initial investment, but overall a PC is cheaper for gaming than any console.
Unless you absolutely must have every game you own on launch day, in which case it depends on the game whether it's slightly cheaper or costs roughly the same, games are pretty much universally cheaper on PC. They also go on sale more frequently [especially if you factor in the indie scene], you don't pay for an online service, you can replace parts rather than having to replace the entire unit if something breaks, backwards compatibility is built in [I'm still using the same copy of Doom I bought in the 90s as just one example], Mods of course, and emulation if you're into that.
It's also worth pointing out that neither the PS4 Pro or the Xbox 1 X actually does true 4k. They both use checkerboard rendering to achieve the resolution. A PC with the right hardware can do true 4k.
That's better than 1080p, but it's still upscaling and not the real thing. It sacrifices detail and motion clarity, as well as being more prone to artifacts.
It's also worth pointing out that the hardware improvements will likely help load times over the older model consoles. That's about all you're really going to have over the older models as games still have to be compatible with the older versions of the console. So the old hardware will still be holding the software back despite the new specs on the new versions.
Unless you're really into the handful of exclusives that consoles have and absolutely have to play them, there's really no good reason to get a console over a decent PC.
Even the size argument doesn't pan out, as you can easily build a console killer PC with roughly the same footprint as a console, and the audio/video connections will be the same. You're using HDMI out either way, especially if you're hooking it up to a 4k screen.
You can even use any kind of wireless gamepad for PC if you prefer to play that way. I have an Xbox 1 controller, an Xbox 360 controller, a PS4 controller, and a Steam controller that I use fairly frequently depending on what kind of game I'm playing.
PC is the most versatile platform out there and you can build to fit your budget and needs.