I've come across this a few times with Subbly clients. I build new sites for them. Largely I use my own template (Good Skin Care theme) and then rebuild it with a new style/theme/color palette. One current client has a great library of content and articles that need to stay. So the way the system currently is, I have to make a choice for their project... Do we build a new site away from their current site and sacrifice all their database of content (media and articles) or build a new site live using unpublished pages on their existing setup. In this scenario, I cannot make the ultimate changes I want to for the design (e.g. new fonts, header/menu), nor the blocks I designed for my existing theme... i have to rebuild them.
This isn't ideal. It would be great, for longevity (e.g. client sticking with Subbly's builder) if we/they could revamp site designs and overlay them onto existing media libraries they've spent months or years curating. Then we can design new sites that are completely customized in preview mode for the client and simply overlay them, once approved, to push live. Hope that makes sense. Maybe the new website builder that's in the works speaks to this issue. It's really only an issue for us designers and long-term users of Subbly who wish to revamp and improve, without having to use a sub-standard pre-built theme/site design that they are not happy with and strip it apart.