I am not sure short paid messages would really bloat the blockchain. Just few additional hundreds bytes per transaction with increased fees. Though it is correct: miners are not the only ones who carry costs. Probably full nodes could prune old messages or messages that are not addressed to them (just to save some disk space).
Update: though probably you are right, it would cause problems (not only blockchain size, but also copyright infringements, propaganda of racism and other extreme cases of freedom of speech)... Probably better to have messages separate, maybe to integrate with IRC (AFAIK bitcoind had some code to deal with IRC already).
The thing with "pruning" is that, as far as I understand, it deals only with storage,
not with bandwidth.
Pruning doesn't really "dislodge" old spent TX from a block (that would screw over the hashes
)
It just allows you to discard obviously "spent" stuff after you have recieved it (assuming you follow the "trust no one" doctrine of Satoshi client) - but if the blockchain has bloated to 2 TB due to everyone and their dog putting a message in it, you would still have to download it (somehow).
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... )
Just say no to feature bloat.