Very good point from another point of view. We also say, "the eye of the tiger"; "hair of the dog". In this case, it means opinion, but if you say the two, "Beauty is in the eye of the beholder" and "Beauty is in the eyes of the beholder", "eye" just sounds more knowledgeable, it sounds like what it's meant to be, "a pearl of wisdom". And it's probably an old phrase, from a time in history when English people tried very hard to sound educated and poetic (probably to get women haha). It's not a description, "beauty is in the eyes", it's a saying, and the person's eye, is their opinion. It is a bit confusing if you take it literally, but it's just a saying. Some things in English are better off copied and not constructed :) they're the ones which don't always make much sense. But as I say, the important thing to remember here is that "eye of the beholder" means "opinion". We also say, "she's definitely giving you the eye!!" meaning she looks at you with affection. Why not give her the eye back so she has two again haha

There are many idiomatic constructions that do not follow proper rules.. I have noticed things like this in Spanish a lot. There are also regional slang usages that are completely incorrect in terms of grammar. The important thing about grammar is to learn general rules with it. Once you are there, I would say not to stress so much abour grammar. Remember, languages are not just a science... They are also an art. What I mean is that there is a lot more there than simply a bunch of rules. : )

No, the best way I can put it is that eye is meaning an opinion here.

It's just a manner of speaking. Don't be too fanatical about the grammar.