More like relational databases are outdated. There was one truly committed effort to bring the database model into the programming language - EJB - and there's a reason it's now a curse word. The successful systems of the past ten years have been those that moved away from the relational model, using simple datastores controlled by application code.
I'd bet that there is more code written in the past 10 years that uses SQL, than that which uses "simple datastores". You don't hear it much, because it just works, all the problems are well known (and so are the various solutions & workarounds), and so it's boring. Whereas, "Company X has adopted No-SQL solution Y for its project Z! That means it works!" makes headlines.
Probably true as far as it goes. But I think that SQL is a smaller percentage of systems now than it was 10 years ago, and that the trend continues to be in that direction.
I believe type theory and typed programming languages are very valuable. But if you keep your logic in code and your store as a dumb store then the store doesn't need to know about them.