This example is obviously hypothetical, but for a simple and practical case, consider the use of amnesia-inducing drugs to selectively eliminate traumatic memories; it would be more accurate to still have those memories, taking the time and effort to come to terms with the trauma... but present much greater utility to be without them, and thus without the trauma altogether.

Deleting all proper memories of an event from the mind doesn't mean that you delete all of it's traces.

An example from a physiology lecture I took at university: If you nearly get hit by a car on the street that's an event you will consciously forget very soon. Your amygdala however doesn't and will still send stress signals when you come to the same physical location in the future.

Children at the age of one can't form proper memories that they can remember as adults. That doesn't mean that trauma they experience during that time don't have an effect on their lifes as adults.

In the hypnosis community people who have the tools to delete memories generally consider it to be a bad idea to remove specific traumatic memories. It can mess people up because they still have the emotional effects of the trauma but don't know the reason.