In my experience, lack of communication is way more expensive. But I don't think the manifesto was about minimizing communication, I think it was about minimizing synchronous communication. Issues and comments and emails and chat are all asynchronous - people can ignore them until they have time to deal with them - whereas in-person conversations and meetings and phone calls are synchronous.

I think synchronous communication is incredibly important for big-picture items - here is what we're building, here is what we think it should look like, here is how we think it should generally work - and often necessary for working through tricky problems (pair-programming is a great example of this), but that asynchronous is better for pretty much everything in between.