Forgive me, I oft confuse two parts of the eye which are both part of the fibrous outer layer of the eye. Shall I give you the innervation, vascular drainage, embryological derivative, muscle actions, and fascial coverings in the orbit to boost my intellectual integrity? I can and will if you so please.

Secondly, shame on me for dumbing something down for the sake of not thinking it to matter. Yes there are other animals which have a white sclera. However those are not visible when the eye is in a straight gaze. They typically only become visable when the animal elevates or depresses the eye. To make my point more specific as you so demand, humans scleras are almost always visable and thus useful.

Thirdly, the white sclera has NOTHING to do with widening you eyes in fight or flight situations lol. Not only does your sclera play almost no role in letting light in or absorbing light, but widening your eyes is controled by muscles, specifically your Levator Palpebrae Superioris, your Orbicularis Oculi m., and your Superior Tarsal m.

Its your Superior tarsal muscle which does the "eye popping" when scared due to its sympathetic innervation traveling along the superior division of CN III. Which makes sense as Sympathetic innervation is USUALLY (ill make the distinction to please you) involved in fight or flight.

TL;DR: Your explanation of the sclera having anything to do with widening of the eyes is laughable. Unless you seem to think its an intimidation mechanism, which would be a tertiary purpose at best lol