Assuming that it is safe to do so as far as people not getting hurt, will it damage the electrical equipment?
That is a dumb electrical question ! As you turn any switch into OFF position, it is disconnect a line with current still running through it as you quoted in your question.
To add to the first two good answers switches are designed specifically to make and break the rated current (and to do this many thousands of times without problem). If you simply pull the plug out of the wall, the break arcs occur in the wall socket which is not designed to do this thousands of times.
it can damage certain appliances, yes. for example, it probably wouldn't harm your toaster, but it's probably a bad idea to unplug your PC randomly. you might lose valuable information, files, and you might even cause the computer to act unresponsive or even crash. it all depends on the appliance.
Some appliances like for instance your computer require a shutdown routine in sequence to be happy. Your computer will complain and cry if you suddenly pull the power and the disk or data may be damaged by sudden disconnect but usually nothing major will happen except loss of your photo or video or term paper. most of the hardware must withstand sudden shutdown but it is not a good routine to practice.
