If I were to discharge, recharge, discharge, recharge,..., an electronic equipment, would there be any negative effects?
Batteries have a limited lifetime (including sitting on a shelf) due to ageing and also a limited number of charge/discharge cycles, which depends on the average depth of discharge (at least for lithium ones). Example:

Lithium batteries don't suffer memory effects (forcing you to fully discharge regularly) so it's actually preferrable to discharge it partially like the graph suggests.

I can only tell about users concerns though, I know how batteries work but not enough to say why exactly this happens (that's when experts on the topic come in).

Anyway, the answer to your question is: your battery won't last long. The undervoltage protection circuit will cut off each discharge before it instantly kills the battery, but it will be dead in very little time regardless (800 cycles judging from the graph for that particular battery, or about 2 years if fully depleted and recharged every day).