In my humble opinion (and 10 years of PC development experience)...
Devices of this class/type are not designed to stay on 24/7 in general. In actuality, always knowing the state of a device means less engineering work goes into the product because there is less environmental variability. One aspect of a device's TDE (thermal design envelope) is power cycling characteristics. While heat is generally considered the enemy, the real enemy is operating temperature delta in a device like the WDTVLH.
Because we are never instructed to leave the device on 24/7 or risk losing warranty, we must assume that turning it off is OK. What that means is that the exact opposite of your statement is true. The devices are designed/engineered to be powered up and powered down and perform as designed it's TDE which includes ratings for temperature (and humidity) deltas caused by power cycling.
If you want a good laugh, go look at the fine print of the warranty of a PC and you'll also see that you're limited to the altitude at which the device is warranted.