Add displays that are not attachments, blocks, feeds or pages?

On certain pages I display a few views via the Insert View module. The views have no attachments, blocks, feeds or page displays. Because I use different versions of the same view for the same purpose, I would like to consolidate the views and use multiple displays instead. But if I want to add additional displays, I have to pick one of those categories. I don't understand why this necessarily has to be the case.

Can't I add a display that does not fall under any of those categories, just as the Master display doesn't? Otherwise I'm stuck with maintaining unneeded features, such as blocks I don't actually need, for example.