What happened to wisdom?
Look up genius in some dictionaries, and you'll see the word "intelligence" a lot. But why can't a genius be one who is extremely wise? Wisdom is one of those words that seems to have fallen out of common language, but I can't see why.
You might think that "wisdom" and "intelligence" are really synonymous, and I'm just making a mountain out of a mole-hill. But I'm not so sure.
To be intelligent is to know what happens to be true. Memorising the whole of wikipedia, parrot fashion, might make one intelligent.
But this wouldn't make one wise. Wisdom has more to do with understanding and insight. It is partly a matter of knowing how truths relate to one-another, and what their significance is.
Why has wisdom been forgotten? It seems to be the correct word for a desirable state of mind, and one which some people still aspire to.
Emphasis on intelligence just seems to ignore a whole realm of what it is to have a grasp on how the universe is.

Sage
While granting your broader point, I'm puzzled by your asking why the word that means 'extremely intelligent' doesn't also mean 'extremely wise'. A simple explanation is implicit in your post itself: these are two different ideas! Why would we use a single word for both?
I think your question should instead be why people are more excited about geniuses than sages.
Well, I take "genius" to
Well, I take "genius" to really mean something like "one with extraordinarily great powers of mind", and that something with that meaning should really be explicable in terms of both wisdom and intelligence.
But I take your point that people might not understand it this way, and that your final question might be a better way to phrase the point for such people.
Al
Genius
to me genius is associated with a definition related to IQ tests and standard distributions etc. It refers more or less to processing power ideally tested against pattern recognition as opposed to anything cultural. Maybe it is that sort of maths/science influence that is bothering you (pulling the definition in a certain direction).
I prefer the sorts of definitions of words that are value neutral, if possible (of course words like 'good' can't be value neutral), because I expect it would make debates easier.