I believe that Bitcoin should follow its initial design goals, and should not try being everyone's everything (chat client, name resolver, distributed evernote, torrent seeder... )
Absolutely, but limited encrypted messaging attached to a transaction looks like a core feature of a payment system. Traditional payment systems also have this feature.
In addition, it would be useful to have an application that adds intrinsic value to Bitcoin, as discussed on
this page on the bitcoin.it site. The specific application could be something like Bitmessage, but with its PoW scheme replaced by Bitcoin postage.
It would also be nice if the protocol could be layered somehow, with a base layer dealing with generalised notarisation services, and several specialised layers on top of that. Below the notarisation service you could have a generalised message sharing layer and below that a generalised P2P layer that deals with peer discovery and perhaps anonymity. It would also be good to share these layers with other P2P applications like Bittorrent, Tor etc. Sharing the more basic layers with other P2P protocols gives you critical mass, robustness, economies of scale and less duplication of effort.