Combat Fleets of the World (16th edition, 2013), now also an older book, list SPQ-9B in the chapter "Three-dimensional air search radars" and claims it to be an replacement for TAS/Mk 23.

And actually it was originally mainly on ships not armed with guns, but with Sea Sparrow or NSSM.

I have not seen the official reason why it was added to some Arleigh Burke. It make sense for the older SPY-1 ships, especially if they are tasked with ballistic missile defence which limits their anti-ship missile defence capabilities. But also newer ships and even SPY-6-equipped Flight III have SPQ-9B - I assume based on the realisation that a dual band radar system (X band and S band) is superior to a pure S band radar.

Software can improve a radar and add new functions - but the physical properties of the radar also matter. The usage of X band and S band radars on the newest Arleigh Burke could be an argument that software optimisation alone is not sufficient.