Summary: After some research, the reasons seems to be due to the SATA-USB controller inside the enclosure. The oscillating pattern is unusual behavior, but without a technological explanation whether this behavior will hurt the HDDs remains unanswered.
I tested with several HDDs using the enclosure and all of them exhibit the oscillating behavior, as such (this time using Sandra)
This (could have) ruled out the possibility that the enclosure wasn't able to keep up with the transfer rate, since using a slower drive didn't prevent this issue. Of course to be conclusive some experiments must be conducted but I don't know how.
Out of curiosity I tried a firmware flashing tool from the controller manufacturer's site. Surprisingly just after I read (no flashing involved) the ROM chip of the controller, the oscillating behavior disappeared, as such:
After a reboot, though, the behavior returned. Dumbfounded, I reported this issue to the enclosure manufacturer, and they responded it was an IC design issue on the controller manufacturer's part. I'm still waiting a response from the controller manufacturer (though unlikely since they deal with vendors not general consumers).
The last resort would be to flash the controller firmware with a newer version I found on the controller manufacturer's site, but this is a risky operation.
