I have tried HD Tune Pro which reads smart data from both disks. It's working fine. And I tried this and Speccy on 2 different systems. So there is high confidence the issue with with Speccy.
It seems that Speccy is polling the disks every 10 seconds or so in older versions, at least in 1.21.491. So therefore I didn't notice it.
In this new version 1.22.536 disk polling takes place every second, or even faster. And thus it is constantly writing a log or causing disk activity. Some disks do internal activity when SMART is polled.
And in the case of error, and I don't think that's happening here, Speccy should go quiescent and alert the user.
I don't understand the reasoning behind why disks have to be queried realtime every second?? It doesn't make sense. Any program that does this should have a user-definable interval and/or default to 1-minute or more.