TL;DR: There is no actual reason to require Apple TV hardware to broadcast workouts on a TV. Period.
This whole thing is just so disappointing. I decided to finally activate the trial and learned what everyone else here already knew the hard way. It just seems so stupid to omit this feature.
I don't believe for a second it's a DRM thing. This is Apple we're talking about, they control every aspect of everything they own (see: Apple v. Epic). There's no way trainers wanting broadcast restrictions (mentioned a few times in the thread) are dictating the availability of AirPlay workouts.
And I don't see how there would be any technical limitations with the Watch metrics overlay using screen mirroring from your device's core OS (vs. an AirPlay control tied to the video itself)–It's literally just broadcasting what appears on your iPhone/iPad screen on a TV.
I totally get that many love Apple TV hardware, and that's cool. But it's a choice, and in terms of functionality, generally redundant for anyone who owns a TV manufactured within the last 5-ish years. Or, for those who just need a few streaming apps, a gaming system. This is Apple trying to railroad people into buying another piece of hardware (I'm not trying to act surprised about this, just calling it what it is) for the full experience, even though the software alternative that could deliver the same experience is their tech and fully within their ecosystem.
My personal use case:
For space/logistical purposes, my bedroom is the best spot in my apartment to use for workouts like this. I have no actual need for a TV in there, but keep my old 2007 720p Dynex set up as a streamer just because it still works. I kept my 2nd Gen Apple TV (which was useful when this was my main TV) set up with it until it started randomly rebooting when streaming content a few years ago. Considering the age and sparse use of the TV, I opted for a $20 Fire Stick instead of a new Apple TV. I pulled the ATV out just for AirPlay (that function still works great) with this the other day, and you know the rest. There is absolutely zero need for me to buy another device, especially one that is way too OP for this tv, just to follow a few workouts a week on a larger screen. But there's also no reason for me to subscribe to a service like this when it's otherwise limited to a screen the size of an iPad at best.
And even if I were to use Fitness+ in my living room, I have a brand new Bravia wit AirPlay built in and, as much as I hate admitting it, a solid Android TV interface. An even without that, an Xbox to handle streaming and a spare HDMI cable/adapter for mirroring. 0 need for a new Apple TV there.
Again, I understand others' milage may vary. And in the end we're talking a one-time purchase under $200, but it's the slap-in-the-face/principle. We've all gotten along just fine without the service until now, and if Apple wants to let subscription money walk away over it, good for them.