I'd go further and say that moving dogs etc around in private airplanes at all is pretty ridiculous. I have done a load of flights for the novelty of it, and if I'm going somewhere anyway I'll look to combine it with a transport, but I can't see the dedicated "lets fly dogs around" charities as much more than a way to subsidise people's flying and owning, using donations. Fair play to them, but let's not pretend it's an efficient use of money. Putting that money into spaying, neutering and local efforts would make a much bigger difference, but just isn't as fun.
It's still better than not doing anything at all, of course.
Whenever I want to do an actually sensible charity flight, I do Angel Flight, PALS, or fly medical people around Africa.