Why is it recommended to not use a device while charging? How does it harm the battery or the device?
It's nothing whatsoever to do with the battery. 

The product manufacturer chose to design the charger/power supply circuit that way. Most cell phones, for example, can be used perfectly well while they are being charged from a cable or wirelessly. 

The power supply is called upon to supply more current if it is called upon to charge the battery and run the device at the same time, so it might cost a bit more, be a bit more complex or be a bit larger. They made their choice, your options are to buy it or not, unless you have the skills to re-engineer it.