That's the old NiMH and NiCad days to get around the memory effect. You should never completely discharge a lithium-ion battery. Doing so will permanently damage it. The battery and/or the device usually has circuitry to prevent a complete drain. Taking a lithium battery down to the allowed minimum charge and back up is okay once in a while to help the charge sensors recalibrate, but don't do it as a regular practice.
Not always to save cost. Sometimes it is to stay within design parimeters. In this case, Apple wanted to keep the new phone (with a significantly faster processor - which usually means more heat and power use), in the same form-factor as the previous phone. Considering that battery life has been a complaint about iPhones since the first gen., I doubt Apple is intentionally using under powered batteries just to save money. Apple has always put design/aesthetics above money saving (which is part of why Apple traditionally has more expensive stuff).
But yes - good advice regarding turning off unused features. They just drain battery (also adding to the heat).
Don’t know about the battery “complete discharge” idea. As battery technology and materials have developed over the last several years - the method of maximizing batter life has changed many times. I think what I have read about (regarding the standard 3G version) is to drain it all the way once per-month.