That isn’t me! I’ve tested it in both ways. Without putting anything into the caption box, there is no alt text. However, tumblr puts the caption into the alt text automatically. If anyone has found a way to get around this, please let me know. But I’d rather be redundant than not have any caption at all.
I put the captions in so that people using text only browsers (such as people who are blind) can still understand what is being said. We may be able to see the picture, but we shouldn’t shut them out of the conversation because they cannot.