Default display of view cannot be used as a facet source

This is perhaps for a very good reason, but it is causing me problems so I figure I have to flag it up!

I am using the TVI (Taxonomy Views Integrator) module to allow the use of a view per-term/vocabulary to override the default taxonomy page. The view I am using for this is a Solr-based search. Given that the Taxonomy module continues to handle the paths, it seems logical to create the view with only a Default display.

However, facets cannot be created using a view's Default display as the source - I have had to bodge things for now by using a Page display, which creates the secondary problem of a having to create a URL for that display which I don't want/need. I also tried an Embed display, which does allow facet creation, but doesn't seem to play ball with TVI.

Can anyone tell me whether it is by design that Default displays can't be used as facet sources?