I'm of the school that one of the worst things Twitter could do is add support for data/attachments, long messages or message bloat in general. The essence of Twitter and its beauty is the messages are short, low overhead and you can skim them very quickly. It compels people to be brief and to not ramble and that is its value and its a good fit for capacity limited mobile. Animated GIF's in Google+ are mostly just annoying.

If you need heavy data then you put a link in the mesage and once people establish they are interested in the subject, then they can go to some server to get the heavy content and all the heavy content isn't centralized at the message service provider.

Also storing and transmitting pictures, video and audio on the message bus dramatically increases overhead, cost and risks of running the service. The second you support it you will have people using it to violate copyrights and laws, you land in a quagmire of shifting standard on what is indecent or illegal in every country in the world. You end up needing a big staff just to deal with take down requests, subpoena requests and to sift though your fire hose to try to eliminate stuff that is going to offend people.

The beauty of short messages is they have very limited capacity to violate laws and copyrights and the message service provider shouldn't be responsile for what is on the web sites the messages link to.

Having integrated image, audio and video support is nice but its actually better if its hosted away from the message bus and decentralized like Twitpic was.