Why is having multiple PhDs frowned upon?
I think your assertion really is an overgeneralization, but there are some negative points to pursuing more than one PhD.

It's the same concern as it would be for pouring an inordinate amount of resources into the wrong pursuit.  It might indicate something about the recipients decision-making abilities, or "perpetual student syndrome".

That said, if that's what one needs to do to pursue the career one wants, that's what one needs to do.

Let's look at two distinct situations.  A college junior starts thinking about her career path, and thinks" 


  I want a very specific, highly specialized pursuit.  I believe that I
  will need two PhD's to establish my credibility and skill set for this
  path.  I am setting out to get two PhD's, and have a good plan for
  doing so.  I've already considered whether I can acquire the skills
  and knowledge by doing one PhD, and then endeavoring to cover the
  shortfall by some other means, and I don't think I can.  I'm well
  aware that some of the skills I learn during one PhD will be redundant
  with what I learn in the second, but there's absolutely no way around
  it.


Contrast this with a senior, who doesn't manage to get a job, so enters graduate school -- gets one PhD, doesn't see the career prospects, then gets another PhD to fix things.

Clearly, the first situation is better (though, I'd argue, exceedingly rare, and often unnecessary).  The second situation is much more problematic, likely more common than the first, and arguably, what some people tend to think the path was when told someone has two PhDs.