You get used to it. I don't even register if a horse has white or brown sclera anymore. However if humans suddenly started to have brown sclera I would certainly notice that to start with!
Of course he might pass it on, however I've not read any concrete research into the genetics of it, whether it's recessive, dominant or a combination of genes. TBH it's the absolutely least important thing when deciding if a horse is worth breeding from. It has no bearing on the function of the eyes, the conformation, temperament, ability or trainability of the horse. It's irrelevant IMO.
But it is relevant if you think it is ugly? It would be like using a grey stallion if you definately didn't want a grey foal.
If I was looking for a stallion for a mare I would choose one that ticked all the boxes, and in my view if he did not have a handsome head and a nice kind eye I would not use him.
Pink skin is more suseptable to sunburn and photosensitivity.
It really is irrelevent in terms of function and is not a weakness. A better comparison is say the agouti gene that makes black horses bay. If you prefer black to bay or bay to black, it's purely a cosmetic and an aesthetic preference just as the sclera colour is.
Plus handsome is as handsome does. CM has one eye with white sclera and it hasn't stopped her from looking after her disabled rider for many years.