But why it has to be longer? Cant they bend light sharply enough to use big glass in a very short lens? What are physics restrictions to this? (Just curious 
, an article regarding this would be an interesting read)
Material properties restrict how much the light can be bent. To make fast aperture short lenses, you'd need new glass-like materials that have a higher index of refraction and have lower chromatic abberation properties. Diffractive optics with their gratings can bend light more than traditional optics, but the technology is not yet good enough to deliver comparable or better IQ.
Due to my poor eyesight I have very high index of refraction lenses in my glasses to avoid having to wear ridiculously thick lenses on my face, and there's a slight lateral shift at certain wavelengths; bright red and deep blue objects appear to be in a different physical location than they actually are when I look through my glasses at them. The worst part is, the index of refraction is only slightly higher than "traditional" high index lenses. The diminishing returns are pretty dramatic.
Physically there's nothing actually stopping you from almost perfectly correcting such an image, but as the index of refraction goes up it gets more and more complicated, and you'd have to have a large number of very, very thin lenses to make it work, and the cost involved would be crazy.
