I don't think personal computers will go away, but I think the era of "put it together yourself" commodity PC parts is likely coming to an end. I think we're going to see manufacturers back out of that space as demand decreases. Part selection will become more sparse. That will drive further contraction as the market dries up. Buying boxed motherboards, CPUs, video cards, etc, will still exist, but the prices will never recover back to the "golden age".
The large PC builders (Dell, HP, Lenovo) will continue down the road of cost reduction and proprietary parts. For the vast majority of people pre-packaged machines from the "big 3" are good enough. (Obviously, Apple will continue to Apple, too.)
I think bespoke commodity PCs will go the route, pricing wise, of machines like the Raptor Talos machines.
Edit: For a lot of people the fully customized bespoke PC experience is preferred. I used to be that person.
I also get why that doesn't seem like a big deal. I've been a "Dell laptop as a daily driver" user for >20 years now. My two home servers are just Dell server machines, too. I got tired of screwing around with hardware and the specs Dell provided were close enough to what I wanted.
There are upsides here as well! I think of things like the NUC or Mac Mini - ATX is from 1995, I'm hopeful computers will become nicer things as we trend away from the bucket-o-parts model.
I'm very excited about the Steam Machine for the reasons you mention - I want to buy a system, not a loose collection of parts that kind-of-sort-of implement some standard to the point that they probably work together.
What are the upsides? You just listed a few things that you subjectively like, but not why they should take over all parts of the PC market. The only factor I can think of is size, but those small all-in-one computers are already widely available now without the need to hollow out the custom PC market.
There's nothing wrong with ATX or having interchangeable components. An established standard means that small companies can start manufacturing components more easily and provide more competition. If you turn PCs into prepackaged proprietary monoliths, expect even fewer players on the market than we have now, in addition to a complete lack of repairability and upgradability. When you can't pick and choose the parts, you let the manufacturer dictate what you're allowed to buy in what bundles, what spare parts they may sell to you (if any) and what prices you will pay for any of these things. Even if you're not building custom PCs yourself, the availability of all these individual components is putting an intrinsic check on what all-in-one manufacturers can reasonably charge you.