Sorry, but that's not entirely accurate.
Going back to the 80's, 90's and into the 2000's, PC 's (Personal Computers) were all designed as a utility for what you described as the "routine work" with some capacity for playing games on them. However, and very recently, PC's changed. And they changed because they had to.
The utilities these large, impractical and expensive devices became more accessible on newer devices like cheap laptops, tablet computers and phones. Even offices began using more efficient servers with connected workstations rathen than individual computers. The Utility PC, us pretty much dead.
Gaming PC'S, or at least as we know, are also comparatively new. Obviously, PC gaming itself is not new, but the technology that defines them today exsist because gaming is why and how PC's stayed relevant in this modern age. The utility capacity for PC's is not lost, so technically @skyfireisn't wrong, but it's not really an advantage anymore. The point is you don't need a gaming PC when a simple notebook or even tablet can do the utility work just as well, so that doesn't sell PC's anymore. The only thing traditional desktop computers still exist for in 2020 (and most of the previous decade) is gaming. The expensive, arbitrary luxury that is the Gaming PC.
It's also perfectly possible to stream from a console as well, so I really don't know you said that. And combine a simple laptop with a game's console and you would have the bases covered and it still cost less than a gaming rig, making PC gaming still more expensive.
@Crazycrabtouched on how PC game deals don't make the platform much more affordable these days either. It's just not as good as it used to be with digital console games having more competitive sales and the advantages of physical media, but there's another factor. People have lost the difference between cost and value. Value us defined buy the individual as to how much said product or service is worth to them, so each to their own to define it. Cost is simply what one parts with for that service, it's a simple fact that cannot be debated, and that's whare the PC has a problem.
Yes, it's very possible to draw better value out if the fact PC's do still have better game deals and the fact you don't pay to play online. However, you only get that extra value back a little bit each time you buy a game, so to offset the significantly higher cost of the hardware, that means buying a lot of games. That COSTS more money, even it it may offer more VALUE, see the difference? For someone who would buy a few AAA titles and exclusives a year, that would just not be worth it.
In conclusion, the PC is more expensive. By miles.