That sounds great and all, but really to what end? What benefit do they gain from spreading the fear? They aren't trying to rule with an iron fist or something. They just want to kill everyone and turn them all into dead soldiers or white walkers (like they did to the baby). If anything, letting survivors go and spread the word that they are coming only decreases their chance of success, as it lets people prepare.
The part that particularly confuses me is that they witnessed John Snow kill one of them, and still made no attempt to kill him once he was 30m out on a freaking boat they could easily reach in some way. Without question they would not have wanted to let him leave with that weapon still in his possession, as I'm sure they are aware of their weaknesses from the last time they were defeated and would want to capture one of the rare swords that can stand against their weapons.
If they'd just changed the scene even slightly so that John killed the white walker in the hut and out of sight of the others, then even that small difference would make it more understandable. You could then just call it an act of arrogance letting the stupid men escape without any worry, as they'd just slaughter them another day. Once they saw John kill the white walker, capturing that sword should have been their primary goal at all costs.