Surely Allah sent revelation to Prophet Dawud pbuh that was needed for that time .
In my opinion, the Law Moses brought to his people was too much for them. But then again, it was their own fault that the laws became too strict. We can draw from their attitude (about sacrificing a cow) when they asked too many questions, like what color, male or female, size etc etc to the point where had they just done it, it would have been much easier, but with all their questions it ended up making it very hard for themselves.
No doubt (my own reading of it here) when Moses gave them the commandments, they questioned it all and as a result ended up being restrictive again. After a very long spell of self rule and free to do as they liked (save to call the Pharaoh god) to be suddenly given strict commandments was just too much for them. They rebelled! Added to that, the stern nature that was Moses made the religion a real 'chore' no doubt.
Hence, as sis Muslim Woman puts it, what was needed for that time was a 'sweet and gentle' reminder for people to 'reconnect' with Allah, and the sweetness of David's voice singing the songs of praises soften the hearts of the Jews after the shock of the laws given by Moses...
Again, this is just my interpretation.
Peace :shade: