Is it advisable to have many clickable hyperlinks in an academic CV?
I agree: most academic CVs do not have a festival of hyperlinks.  I don't see a problem with it, unless -- as @Taladris says -- the large amount of hyperlinking creates clutter in the document.  For something like a CV, where the spacing on the page is highly adjustable, I would think that you could probably have even a highly hyperlinked CV and take a little care to make sure that it does not look too busy to the eye.

I can tell you though why I don't feel the need to hyperlink my CV (and I imagine the reason holds more generally).  It's simple: I also have a webpage, and anything which appears on my CV which could get linked to also appears on my webpage.  Further, the translation between the two is straightforward: I have a section of my CV listing papers, and I also have an immediately visible link to a subpage containing papers from my main webpage (which, as you can see, is no frills to say the least, but it seems to get the job done).  

Although I am certainly no expert on the visual display of information, webpage design (you'll know that immediately if you clicked on the above link) or anything like that, it is my opinion that a webpage is a more natural medium to have clickable content than a CV.  

I think every young academic should have a professional webpage.  If they do have one, I'm not sure that a heavily hyperlinked CV is necessary, although again I see no harm in it.