In more general terms... if ~technology has been getting better with some short doubling time for hundreds of years... why is it that the NEXT doubling is supposed to be the really significant one?
But generally, I agree. We're biased to under-appreciate the impacts of past changes.
For example, that bit about instant access to people and knowledge was probably said about the telegraph too.
Which is not to say that internet technology isn't widely more crazy than all of those previous or that there won't continue to be wider and crazier things to come. It is to say that we're not escaping exponential growth and there still isn't anything like a spike in that sort of curve.
The singularity theory proposes an increase from exponential: some technology that speeds new technology's ability to speed new technology. Without the feedback --- without the efficient feedback --- everything "stays exponential". Which is only really depressing if you're looking for hypersmart AI and endless free human life in the next 20 orso.