It would free things up so much - the backend team can focus on JSON/HTML templates, the designers can work directly with the website without necessarily going through dev (for better or worse ;), marketing can add all their little trackers, easy to outsource parts, and you could build up an entire cross-language ecosystem of plugins that manage anything from user accounts, billing, wikis, blogs, knowledge base, admin CRUD systems, ... yet it's all on the same site from the end user's perspective.
I think there are multiple enterprises that have (also re-)invented this architecture, but I haven't seen any serious open source offering that focuses on this type of use.