Why are underhooks so advantageous?

hips/shoulders control. (standing) In Judo, the ideal position to do many throws from is essentially a clench, with as little space between each other as possible. If I get double unders on a guy, our chests are together, I'm lower than him, and he can't get away or get low--all excellent factors contributing to a good throw for me. Keep in mind that I can pull my arms down at my leisure, as they are below his, but he can't pull his arms up and away easily. If he overhooks to try and keep my arm still, I can usually still pull straight back and out, or I can use his overhook against him as much as he can use it against me. On the ground in guard, very similar principles are applying. A good sweep has you beneath them and close to them, and when you have underhooks, you almost always have both by default. If you're beneath a guy who is on top of you in side control, you are getting out and away from his arms--if your arms are under his armpits, that means he isn't controlling your hips with anything except for perhaps a single knee and laying down on you. If you shove your arms up against an immobile guy above you, you are pushing yourself down and away from him. Your arms are also blocking his from chasing you as you get away, making your hips mobile enough to spin around and get your legs between you. The reason it's not really helpful when you're mounted is that he is controlling your hips with his knees. tl;dr double underhooks = you're lower than he is, you're close to him, you're preventing his arms from being effective, you're blocking his arms from being where they want to be.