I do a lot of closed caption fixing as part of me job and I don’t see a clear path from Premiere’s internal caption tool.
One issue is there is a lot of formatting with Open Captions that will not transfer to other standards. With closed captions all you can do is set the color and placement of the text. (Adobe’s Open Subtitles works the same way).
You can Export Open Caption clip from the bin into srt and xml. I did a test and the srt will not import into MacCaption, which is the program that I do a lot of conversion with. I can bring in the xml but the placement is not correct.
What needs to be remembered is that every different playback and delivery method needs a different type of file. DVD, BluRay, youtube, web players and what not need different files.