This is the outcome that we will have or willing to have. Oops it didn't happen! so; Although this is not the outcome that we would have desired , etc would is the past tense of will. Your sentence: Although this is not the outcome we have desired. This is grammatically correct but misses the nuance of what we were willing to have. You place the emphasis on desired. It misses the emphasis on what we 'wanted' to have happened.

In short, that depends on whether it is real or imaginary.