Hmm, I am slightly confused, here is my confusion:
I didn't quiet understand why the narrator would like to continue being perfect strangers, or rather what exactly did the narrator meant with a perfect stranger?
For myself, an stranger is someone who we haven't met, so in that sense, I would think that in this poem, the narrator would have liked to have not met that someone. In a way, I feel that perhaps the relationship didn't quiet work, and both got separated. Perhaps, lust was the main portion of the relationship rather than love? And perhaps, if both would have remained strangers, there's be the possibility of seeing each other?