Yes, and no.
Yes: REST / JSON is nice. I've used them widely as a kind of cross-platform compatibility layer. i.e. instead of exposing SQL or something similar, the API is all REST / JSON. That lets everyone use tools they're familiar with, without learning about implementation details.
The REST / JSON system ends up being a thin shim layer over the underlying database. Which is usually SQL.
No: databases should NOT be flexible, and "NoSQL" has a very limited place.
SQL databases should be conservative in what they accept. Once you've inserted crap into the DB, it's hard to fix it.
"NoSQL" solutions are great for situations where you don't care about the data. Using NoSQL as a fast cache means you (mostly) have disk persistence when you need to reboot the server or application. If the data gets lost, you don't care, it's just a cache.