On the heels of David and his illicit and horribly unclean rondezvous with Bathsheba, this Psalm adds the the very heavy Old Testament tone for this Sunday. It feels like it wants to add to the notion that the OT is nasty and the NT is happy clappy, but to assume that is to miss the entirety of the Psalm.
Even as "there is none who have done good..." God still promises deliverance for his people Isreal. Grace abounds, even in Psalm 14. I haven't done the research myself, but if I recall my Hebrew Bible from seminary, there is nary a word of judgment in all of the OT that isn't followed in due time with a word of hope.
God has always, is always, and will always be about restoration - even when it seems as that there isn't a single person left on earth who desires to do his will.