It's not due to imprecision, it's due to design and fundamental optical constraints. There's nothing special about the optics used for a push broom imager, it's

It's not due to imprecision, it's due to design and fundamental optical constraints. There's nothing special about the optics used for a push broom imager, it's just an ordinary lens. If you put a full frame sensor at the focal plane you could take an image of a several kilometer square patch of Earth. If instead you put several different lines of sensors in the focal plane and put each behind a color filter then you'd have a multi-spectral push broom sensor. But each line does not view the same part of the Earth at the same time. Because the sensors scan the Earth they end up imaging the same spot within a fairly short delay. But optically it's not possible to have each color line viewing the same horizontal slice of the image of Earth at the same time, that's not the way lenses work.