Sava's answer is correct, but I wanted to respond to part of your question.
But why is that? As far as I can see, it's got a single way down...
You see it as "only one way out". However, someone who is defending sees it as "only one way in", which means that when you are able to defend this chokepoint, you can keep everyone safe.
This is exactly why castles have a wall and a handful of gates (or often just one): the less gates into the castle, the more resources/manpower you can dedicate towards defending these gates.
To paraphrase The Man In The Iron Mask, when the commander explains to the king why they cannot beat the four musketeers who are entreched in a hallway: "The chokepoint of the corridor negates our superior numbers".
with lots of steps
The civilians won't be moving much when they're in there, why would the steps matter?
& poorly lit.
Again, there's little reason for the civilians to need good lighting while they're hiding. They're not doing anything. I also don't see why they couldn't just light the crypts better if they really needed to.
Additionally, for a human enemy, should the enemy enter the crypts, it makes you more likely not get spotted when you hide. Or even when you do fight back, your eyes are used to the dark and the enemy's are not yet, which again gives the defender the advantage.
Why would this be the safest place?
Because statistically it has been. Consider that White Walkers haven't been seen for a thousand years, but human wars have happened pretty much every generation. This is a centuries' old habit: hide the civilians in the crypts, because it's the best place to keep them safe from the battle that rages on outside.
There is a strong consensus on the tactical benefit of hiding the non-combatants and to keep them safe. This is for two reasons: the soldiers don't need to worry about the safety of they family and can instead focus on the battle, and keeping the civilians safe means they can assist with the post-battle fallout (tend to the wounded, clear rubble, restore things).
They did it in King's Landing with the Battle of Blackwater Bay (it's the scene where Cersei talks to Sansa about having instructed the guard to kill her and her children should the safe place be breached, so that she is not taken by the enemy). Jumping to another franchise, one of the best known use cases of this tactic is in Lord of the Rings, in the Battle for Helm's Deep.
You should consider this safe place as a "keep within the keep". They are the second walls, when the first wall is taken by the enemy.