What do you mean by essential implication? Here is how you explained your interpretation -

I always took "Spring's a girl in the streets at night" to refer to prostitutes who would start appearing the streets when weather permitted

My mention of prostitutes not taking time off on dark winter nights has a direct bearing on what you said. Had you not mentioned the weather at all I would still have disagreed but could see how you may have come to your conclusion. But you didn't. Your interpretation seems to be that spring is heralded by the appearance of prostitutes! That is what does not make sense.