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I'm not sure a successor to SQL is even necessary, rather there would be benefit to some higher level interfaces provided by the RDMBS that compliment SQL to cut down on the egregious application boilerplate that becomes necessary to achieve common tasks using SQL directly.

SQL is essentially the assembly language of the database. That makes it very powerful, but sometimes you just want a language that gives you a "garbage collector" for free, while still being able to drop down to assembly when you need additional power.

There is no technical reason why an RDBMS can't support different modes for accessing data. We are just so used to putting that work into the application that it has become a hard sell to want to move it to the right place.