To switch the miner on and of regularly does not affect it at all. I have miners that are used as heaters and they are turned on and of several times per day. Also rental miners turn on and Off, depending if they are rented or not.
The humidity could be more of an issue, but from what I have heard bitcoin miners are operated in every climate zone of the world and often even in warehouses/shipping containers where there is also a high humidity.
This is what I was thinking when I saw the news about variable load grids and bitcoin miners being shut down to help manage power, surely it can't damage them too much otherwise no one would be putting there miners at risk for this?
If you switch them off locally, it is not a problem. Damages are possible, when they cut power on the whole line. Or on a general blackout.