Whenever a planet gets a reinforcement pulse, the pulse's budget is increased by 10% for each guard post. So, killing guard posts on a planet reduces the rate at which the AI can generate ships at that planet. This was added in version 7.023, I believe, wasn't documented in the patch note but Keith mentioned it here:
http://www.arcengames.com/forums/index.php/topic,15466.msg171590.html#msg171590There's also a cap on the maximum number of ships the AI can reinforce onto a planet, which goes down as you kill guard posts. It can still reinforce the planet after it hits the cap, but it will do so by merging ships into higher mark ships rather than adding more ships, which is less efficient.
Each planet also has a cap on the number of defenders it will maintain, and if it reinforces above that level the excess ships get released as threat, which will then tend to wander into your territory to cause trouble. Neutered planets will typically have their maximum number of ships reduced below this level, so they'll generally not produce border aggression.
So, neutering planets greatly reduces the danger associated with having planets alerted for very long periods of time. Any AI planet next to a system that isn't AI controlled (and doesn't have a Warp Jammer command station) will be alerted for the rest of the game, and is probably worth neutering if it isn't a Rude Gesture planet (the ones with four warp counterattack guard posts).