The single pivot sidepull design requires a fairly wide pad gap at the rim in order for centering to not be too finicky. It's essentially the widest of all common rim brake designs. This is due to the spring design's two sliding contacts, as Jobst Brandt writes about here. The contacts are hard to keep at the exact same level of friction, and any disparity takes the brake out of center. You need a wide gap to compensate.
You can't just add longer actuation arms to make the same design more powerful because it's still the same human hand at the lever end. Longer actuation arms with the same pad gap would require either shorter lower arms, which you can't do because there's a tire there, or a lever that pulls more cable. You can make the lever pull more cable, as in a v-brake lever, but note that v-brakes have a much smaller pad gap. That's why they can have a lever that generates much less mechanical advantage. Do the same thing with a hypothetical long-armed single pivot and you get a brake with very low power.