I've looked into this issue a bit more. I think it's worth nothing that there are two heart rate sensors, as this document explains:
Your heart rate. What it means, and where on Apple Watch you’ll find it. - Apple Support
The green LEDs are used when you are in workout mode; they are more or less accurate, though I found a number of data points that were way too low or high. The second set of sensors is infrared. As Apple says in the document:
"The heart rate sensor can also use infrared light. This mode is what Apple Watch uses when it measures your heart rate every 10 minutes."
It's a bit funny that it still says every 10 minutes... But that's the one they turned off, at least when you're moving. So, to me, it seems that these sensors are simply too unreliable when people are moving, and rather than report faulty data, they turned off the feature. Frankly, I'd expect them to find a fix, and, if necessary, replace the watches so this feature works.