Actually it's not bad at all much less "horrifying", that's all old wives tales...
It's not bad for the phone, and whether it's bad for the battery depends on the battery technology. In fact previous battery technologies were recommending the occasional full drain!
For lithium-ion batteries the kind used in the iPhone draining to 0% can indeed strain them (though less than you think, as shown by research), but the iPhone doesn't let them go to 0% anyway. It switches off way before that (even if it shows it as 0%). Mind you that regular use cycles (defined by Apple as using 100% of a full charge, even if it's broken down as going from 100% to 80% for five days and recharging) also strains the battery. You cannot not strain it, all current technology batteries degrade over time.
Also note that getting lithium-ion batteries to 100% and keeping them charging can also harm them (although modern devices have mechanisms to prevent that). In general it's advisable to keep going from 80%-20% and back, than to go all the way to charged (or down to 0). Same, one should not store long term fully charged.
But most of this is irrelevant micromanagement unless you plan to keep your phone for years and don't ever consider replacing the battery. Even so, the battery lifespan vendors like Apple give is around 3 years of cycles.
All in all, you can fully drain your lithium-ion iPhone battery as often as the average person does (e.g. just avoid doing it all the time), and you'll see no special degradation. It will run its cycles and will degrade by regular use after a few years even if you never let it drain (and you can trivially replace it with a new one).