This is roughly the path I'm taking on my current project. There are some things that have a consistent, "traditional" schema. However, many of the feature-important things are being stored as JSON blobs. This means that I don't have to worry about schema migrations when I add a new feature; instead, I just define its JSON schema. This works particularly well because I don't need to join on these items. The downside is that I do have to do occasional manual processing on them (sum up all values of type FOO) that would be trivial if everything were perfectly normalized.
I looked at that (and have done that in the past), but I really missed some of the ORM features I got with relational. I would up writing more glue code than I liked for things that would otherwise be free. This is my compromise world (and Postgres is getting better at handling its JSON).