Attributives -- he said, she said -- do more than keep the characters straight. They break up the speech. Putting them in can sometimes be a trick, when you don't want to break up the speech. I've had to resort to starting the paragraph with "He said," a few times. But it can break up a speech when a mere period does not seem to give enough space.
Actions can do it even better. Or incidents involving people or things other than those speaking. A gesture, a shrug, a bird warbling in the nearest tree can be useful to remind the readers that this is not some disembodied voices chattering in a vacuum. But it can also help break up speech more elegantly than punctuation marks or even paragraphs -- because more naturally. The nature of speech is to be broken up without consideration for paragraphs and topic c sentences and the like.