It's mainly to reduce EMI. For example, light dimmers, which do not use zero crossing. often will generate the familiar buzz interference in AM radios. The fast risetime that occurs in a non-zero turn-on (as in your first picture) generates many high frequency harmonics which can interfere with other electronic devices.
Also, if you are controlling power, such as a heater, by cycling the power on and off, zero-crossing maintains a higher power factor then using a phase-control (dimmer) type controller. The power companies like a high power factor to minimize reactive power current, which generates IR power losses in the power lines.