I agree with von Suppé.
Whenever I'm creating subtitles myself I put the dash (which in my humble opinion should always be a so called "em dash"
—, not a "hyphen"
- ) in front of the second line, in other words exactly where the change of the speaker happens within the same subtitle.
I also think it's easier to follow such a subtitle if both lines are left-aligend but as a whole the subtitle should of course be centered within the video frame, with the top line not starting before the em dash of the bottom line.
(click to enlarge)
That's what I personally consider "most aesthetic" and easiest to read.
I'm quite sure the main reason for putting a dash in front of both lines is rather just a technical shortcoming because it is easier to format this way. But of course it also depends on what the viewer is expecting and used to.