Most sunglasses do not cover the eye fully. For example, any design where the lenses are close to flat (aviator, retro) or small does not protect the eye from rays coming from above or the side. Sunlight commonly comes from above, so these sunglass designs do not block a significant part of it. If the lenses are tinted (not clear), then they worsen the outcome for the eyes, because the dark glass in the centre of the visual field makes the pupils expand. When that happens, the pupils let in more light from any direction, including sunlight from the unprotected top and side directions.
In comparison, the polycarbonate safety glasses that currently cost 2 AUD in a construction shop have a wrap-around design and large lenses that leave only a small gap between the forehead and the glasses. Light from the side and nearly all other directions has to pass through the glasses before reaching the eye. The material for the safety glasses is polycarbonate, which block 99.9% of UV light. In order for sunglasses to provide better UV protection than the safety glasses, they have to block a larger percentage of UV light or cover more ray paths into the eye.
Suppose that sunglasses were made from a material that blocks 100% of UV. Then to improve on the safety glasses, the sunglasses would have to cover at least 99.9% of the ray paths into the eye that safety glasses cover. In other words, the sunglasses would have to have the same wrap-around design and as large or larger lenses.
An improved design for both safety glasses and sunglasses would take the wrap-around design one step further: cover the eyes from top to bottom as well as from side to side. One way to achieve such cover is a half-dome over each eye that touches the forehead above the eye and the cheek below, as well as the bridge of the nose and the temple.
A brimmed hat that blocks light coming from above compensates to some extent for flat-lensed or small sunglasses. The hat does not protect the eyes from light coming from the side and below the brim, so the classic sunglass designs are still inferior to wrap-arounds even combined with a hat.