When I was in middle school, we were assigned to each write a psalm. Only two of us really did, with everyone else simply writing bad poems. But mine was a cry of despair about the faculty, so I was given a bad grade and forced to rewrite it and make them look good. I stand by my original words; that's how David wrote. It doesn't matter whether he was right or not to hate his enemies "with a righteous hatred" (and remember, this likely included Saul, the king of Israel); that is how he felt and expressed it.
I've recenty discovered a band called Red. They are essentially Christian metal. I like "Let It Burn" particularly, as I consider it much more a psalm as David would sing than the kind of things sung in churches these days. To me, most of today's Christian music is poorly written, and certainly shies away from the realities of pain. I appreciate a band that writes something like this.
And just for the other side of the equation, here's Red's answer with their song "Not Alone".