"If we used CC-BY-SA that wouldn't be a problem, because those letters would
be enough."
Not really: "You must include a copy of, or the Uniform Resource Identifier
(URI) for, this License with every copy of the Work You Distribute or
Publicly Perform."
So you must also include a copy of the license, or the URL where someone
could view it. So "those letters" as you put it would not be sufficient.
"CC licenses have a far more one-size-fits-all nature."
To quote from the GFDL: "This License applies to any manual or other work, in
any medium, that contains a notice placed by the copyright holder saying it
can be distributed under the terms of this License."
Note the "or other work" part so, just like someone quoted from CC licenses
above, the GFDL can be used for just as many different things including music
and videos, etc. and the requirement to provide source gives it a leg up in
that aspect, I think. If you're editing it's much better to be able to back
to the original material and edit that, especially if a lossy codec is being
used.
Anyway, this seems that it's really just a "Why I don't like the GFDL"
thread.