Machines have internal mechanisms, like power sources and servos. The most likely answer is that snapping their "neck" severs the processor from these power sources and possibly severs the artificial muscle fibers (they have those, as per the game's lore) which drive their limbs, so while the robot isn't "dead" and can be repaired, it is likely useless for the next for hours or days. Ergo, from the standpoint of a major war, it may as well be dead as a human who gets his neck broke.
Fridge Brilliance
The Smart Pistol is a compact close combat weapon capable of taking down nearby enemies quickly. A perfect weapon for pilots just like what PDWs are to real-life tank crews: quick to use and small enough to be comfortable to carry in tight spaces. This might be unintentional on Respawn's part though.
Dropships do an FTL jump to evacuate the battlefield when a match is over, but they always fly in first. Because space is big, and this reflects that: it's far safer to FTL jump from atmosphere into space than to go from space into atmosphere. The one time in the story this happens is in the Militia opening of Mission 8, and it was a minor miracle the dropship didn't slam into the ground, especially because the jump calculations weren't complete. And they still got shot down anyway by anti-aircraft defenses. In the first level of the Militia campaign the dropship your character is in jumps into the atmosphere and then descends to deploy its Pilots. This happens in a few other missions and in the IMC campaign you can watch Militia ships jump in. Presumably the FTL tech's been around long enough for the jump calculations to be pretty damn precise.
Fridge Horror
Only the pilots get extracted when the mission fails. All the grunts, the non-elite human footsoldiers? They are simply left behind, nobody cares. Now, considering that both factions actively try to shoot down the extraction ship to kill all the enemies, they probably aren't big fans of taking prisoners... The fact that timer to reach the ship when it arrives is about 10 seconds, it becomes clear that even if the pilots are worth saving, everyone is expendable.
It's possible that allied ground forces evacuate after the pilots are extracted first, in a slightly more organized manner. Spectres may be set to self-destruct to prevent capture by the enemy.
IMC Grunt chatter explicitly mentions extractions. Pilots are probably just a higher priority, being hyper-lethal special ops and all.
There are no known sapient species aside from humans, and possibly AI/machines if we include Spyglass and other things like it. So where did the ruins in "Swampland" come from?
The Militia's 1st Fleet has a number of civilian ships containing the families of the soldiers. Are they there for solidarity, escaping IMC oppression, or to avoid retribution from the IMC?
are to real-life tank crews: quick to use and small enough to be comfortable to carry in tight spaces. This might be unintentional on Respawn's part though.