The main reason I avoid cheap sunglasses is that if they only dim in the visible spectrum, your pupil dilates and lets in more UV light than it would have otherwise, damaging the retina. Not that the full spectrum protection explains away the entire premium, but it is a reason not to go for bottom of the barrel ones sold on street corners.

Common glass absorbs most of the UV light, and your lens and cornea absorb the rest. If UV light did hit your retina, you'd actually notice it - people who lack a cornea and/or lens can actually notice UV light, which is why artificial lenses like you'd get after in cataract surgery are now made of UV-absorbant materials.

So unless you have a rare medical condition AND you're buying plastic lens glasses, I think you're worrying for nothing.