Welll the application is that websites like blockchain.info post analysis for everyone to see— screwing up the privacy of Bitcoin in practice.  I don't have much need for anonymity, but not having everyone from your nosy neighbors to random thieves knowing all your financial activity is both a matter of human dignity and basic safety.  The basic design of Bitcoin should be reasonably private if used right, but people frequently reuse addresses and do other things that gum it up.

Making joint payments can reclaim some of that privacy (but I'm far from convinced that it would thwart serious forensic analysis) and also reduce the total number of transactions being made. 

Besides, there are already many mixers:  But the issue with them is that they're centralized services. When you deposit your coins there is a risk the operator will steal them (or get them stolen). They charge fees... and the operator may be spying and recording all the linkages anyways. With those kinds of properties they're services which are less useful for casual privacy— and only really attractive to the kind of nefarious activity which I don't endorse.

Joint transactions can also be used to have people securely pool funds to pay for common work.  E.g. "I'll post pics with a shoe on my head if y'all raise 10 BTC" and other neat things especially when you factor in the other scriptsig types.