Technically it is bad when you repeatly switch the power supply because of spikes.
In generally it shouldn't cause any serious issues cause power supplies are usually made to withstand some levels of spike.
Back to the issue, it can be caused by crappy BIOS or one of the USB devices acting odd if you have wake on USB turned on.
If you don't use wake on lan/usb, there's also the power setting to auto power on when there's a power returns when there's power failure. You can turn all of those off.
There's also different power modes which you can set to prevent it from waking up.
*Note that if you're using "branded" system some of these options don't exist or can't be disabled.
An example here, can vary a lot depending brand and BIOS
You can also try using sleep mode to see if the system gets woken up.
Then you'll be able to obtain some hardware information about what cause it to wake.