+1
Time travel, regardless of whether we have an open or closed loop, will exhibit causal paradoxes, so we can only demand so much logical coherence from these stories.
At a formal level, closed loop time travel stories are tragedies because they are fatalistic by nature. No matter what the harbinger or oracle tell the protagonist, his fate is sealed. Thus, possessing knowledge in a closed loop dooms you to be an ineffectual Cassandra.
The open loop allows for growth, change, and learning. Time travel for profit $$$ and character growth.
The type of time travel you invoke probably depends on the type of story you want to tell.