I doth not know... but I think I know why Oric wants the Target dead. Fun. Allow me to explain.
You are now
Oric the Awesome. Seeing as the Target is now dead and her body will be unrecoverable for an extended period of time, you are now the main character. You are standing behind your desk. There is a theoretically infinite amount of paperwork here, including but not limited to: the minor gripes and complaints of various Illborn and siblings, lost item reports, lost friend reports, lost item due to loss of friend reports, annual domestic product (measured in Stream Rubies) and miscellaneous financial statistics, mismanaged paperwork reports, death threats and indicators of the brimming revolution, mismanagement of mismanaged paperwork reports, and a very small list of compliments on your work this cycle.
What will you do?
As you can see from all the paperwork in Oric's office, he has a boring job as the warden of the warrens. Hunting down the Target each cycle may be the only entertainment viable for him. The reason he doesn't just go and kill us is because it would be boring. As of now, we are nothing compared to Oric. Bam. And we're gone.
So being the warden of this prison, his entertainment consists of tormenting and tricking us, letting us feel we have hope-and then bringing us down.
In conclusion, the reason Oric wants the Target dead is because it is entertaining for him and his jailers i.e. the Sinister Siblings.
Two more things not necessarily related to this theorycraft: One, that intro to the Oric intermission states "the minor gripes and complaints of various Illborn and siblings" which suggests to me that the Sinister Siblings are not the only Siblings of Oric the Awesome. And Two: did we ever try to Third Shift with our Soul Stars? If we can't, note that Oric may be able to do so as a nasty surprise once we fight him.