I have seen a database that uses an SQL-like language but it is not a RDB. It's said to be much faster than Oracle, but it certainly doesn't need the SQL syntax to work. Needless to say, the speed doesn't come from the SQL syntax. :)
It made me wonder about decoupling the language from the interpreter. Without the SQL characteristic, would anyone be attracted to the MySQL, PostgresSQL, ..., WhizBangSQL systems?
But does it necessaruly tell you anything about the underlying structure and the performance of a database?
If we drop that acronym, "SQL", and still provide a database that handles relational queries (but perhaps uses a different but equally capable language), does that matter? If yes, how much? And why?
One of SQL's remaining powers over most other options is the ability of non-expert users to construct their own ad-hoc reports. This is a big part of why Hadoop has Hive, which incorporates a very SQL-like language, and most other "big data" tools have something similar.
the value of the different database implementations comes from how efficiently they can implement the relational model, and what optimizations they have to support particular use cases, or extensions to make supporting and maintaining them more practical. those optimizations/extensions also lead to some of the differences between what sql might be if it were "purely relational" and what is is in practice.
so dropping sql and using a different language would be more a nuisance than anything. what is important is whether the database is relational or not. and databases that are not relational have been tried - they are (misleadingly!) called "nosql databases" (they should be more accurately called "non-relational databases", of course, given the above).