That's not really true. Lithium batteries have a set cycle count life and it's the same whether you zero out every time or not. The only difference is that the math is dealing in partial cycles not full ones.
The draining it out is more for the software than the battery. Particularly with iOS devices since the same software is running batteries of very different sizes. The meter software can become corrupted just like any other software in the system so a full drain to shut off periodically helps to keep the meter correct so it doesn't report you have battery falsely when it is in fact drained.
All of this though is secondary to the issues of never running the battery (ie keeping it on the charger all the time) or having it drain out and now charging it for ages (which means even the trickle charge drains out eventually). Those two things will kill your battery more than how often you charge it
Properly designed lithium battery chargers don't actually keep trickle charging the battery unnecessarily. Many of them don't even turn on the current flow if the battery is between 95% to 100%, so the issue you mentioned at the end shouldn't happen. (Some will have tricks for refilling them at the end and it's all right, but leaving a lithium battery on the charger indefinitely should never be a problem on a proper charge)
Partial cycles arn't uniform across charge levels.
I recall if you charge from 0 to 10%, you apply more wear and tear to the battery than if you charge from 60%-70% even though they're both 10% of a cycle.
Also, past 4.0 volts, it's best to charge at a slower rate to keep the heat down because then you'd also have more wear and tear than the middle. Do that and you'll keep the upper end wear and tear to a minimum.
Ideally, it's best to keep your battery in the middle 1/3rd but that's not really feasible. Next best is to always keep it as full as possible. Worst is to drain often and then charge it back up entirely frequently.
(I had to design a lithium polymer battery charger a while back for a side project. Got a bunch of research done, but turned out it was much more worth it to use off the shelf components than to actually implement our own so never finished it.)
With that said, I only deliberately do a full drain calibration cycle on my device when I first get it. And always try to leave it on the charger if I can. Oh, and if I have a choice, always the slowest charger I can get if I have the time.
This calibration thing? I'll do it again in 2 years if I still use the device. Certainly not every month.