This argument may have been true 3 years ago but they're all vastly easier to carry around in one hand without getting fatigued now. The iPad Air is incredibly light for its size and I was able to use it for hours at a time without wanting to put it down like the older iPads. The retina Mini I have is even lighter.
I agree with everything else you say though. They're great for consuming web content, but I barely use mine for anything else now. If I actually got a phablet like the iPhone 6 Plus, I would probably end up selling my mini altogether because everything I do on my iPad I could do on my iPhone with a larger screen.