As others have pointed out, there are definitely some flaws with the logic applied here.

> It’s faster, cheaper and still relatively small

Yes, the Optiplex is going to perform better at a lot of things. The prices I'm seeing are around $60 -- the Pi is either $10 for the Zero with WiFi or $45 for the "3" with a reasonably sized Micro SD card. Granted, your needs may include more storage than what's offered by a Micro SD card, so that would set the sticker price higher, but the Optiplex that was linked to didn't include storage, either. But the bigger area where the Pi is going to be less expensive is in power utilization. The Pi is really cheap to run. These things don't even need active cooling to run well.

But it's also not really fair to equate these two devices. It's not even fair to say 'for a home server' -- that all depends on what you're going to use it for. If you're using it as a low power home server for sharing files and/or basic web app, REST service or home automation hub and have no intention of doing processor intensive tasks like media re-encoding[0], the Pi is a good fit and economical to leave powered on all the time. My Plex server, in fact, points to a device that's a Pi competitor which has archived media on it.

Then, there's noise and heat. Provided spindle drives aren't used, Pis are completely silent and generate substantially less heat than a full-sized PC. I am fairly certain the Atom processor in that Dell has active cooling. Even if it's a heat-sink only design, those usually include ducting that feeds off one or more other fans in the device (which end up being more powerful/louder to handle cooling the extra components). Minimally, there's at least one fan running all the time. Yes, you can buy quiet fans (adding to the cost) and nearly eliminate this sound, but in my case, my Pi clone doesn't even have a heat-sink on the CPU. It shares a case with three, rather hot, drives (though I've designed it with ducting and separation to reduce the impact of this heat). It has been running that way for over a year without difficulties.

[0] The specific mention of Plex leads me to believe the author was targeting those of us who want a Plex Media Server on an RPi. I'm not sure how well Plex works on the Pi, but I use my Plex server with a Roku and many of my videos must be re-encoded to h.264/MP4 from h.265/MKV on the server in order to play them back -- I also have to re-encode to a lower bitrate when I'm remote. I'm not confident the Pi could handle those tasks.

[1] It's either a Banana Pro or Orange Pi; can't remember -- I haven't had to touch the hardware since I set it up. It's Ethernet attached with a 1TB SATA drive and two 2TB USB disks. The device handles the task perfectly. In fact, I only set it up because my i5 server case was too small to take on the storage, so I printed up a case to house the Pi clone and the drives. It also serves up a REST service that my SmartThings uses to control my garage door and older Pioneer receiver, as well as a node service that lets my Alexa control my Roku. I even had it set up to run Octoprint to control my 3D printer, but purchased a Pi 3 for that because I wanted to relocate the printer.