Who do you think built Moat Cailin? And why was it allowed to fall into such a state of disrepair that only three out of twenty towers are left standing (even the Wall could manage 3/19!). Even if a southern invasion hasn’t been as much a risk during the last three centuries, it still seems like a nearly criminal amount of negligence considering the amount of safety it provides the North, essentially nullifying any sort of southern land invasion.

The Starks built it.

In terms of why: 

1. It’s still devastatingly effective even without the towers, so it’s questionable how impactful any neglect is. If 200 archers can hold the Neck against an army, how much more defensive multiplier do you need?
2. It’s not clear how much use Moat Cailin has seen in a long, long time. Balon mentions ten thousand years of armies smashing themselves against it, but we don’t have any other historical examples post the immediate Andal invasion of anyone attempting it. Catelyn mentions that the wooden keep rotted away a thousand years ago, which gives us a rough date as to when the Moat was regularly in use. 
3. The Starks had other security threats to worry about – the Ironborn, the wildlings, the Arryns, etc. – that Moat Cailin wouldn’t help with.