Staircases represent a tripping hazard, and it is therefore not unreasonable to illuminate them under certain circumstances. However, as I have shown in the past, poorly designed illumination is actually much worse than no illumination at all. A (literally) brilliant example of this comes from the "Lustgarten" park in Potsdam:
These lights combine both the wrong direction (shining horizontally rather than downward) with being extremely bright, which makes them terribly glaring, and makes it harder, rather than easier, to safely ascend the staircase. (Right after I took this photo, I misjudged the position of the first step and stumbled slightly, even though I was trying to shield my eyes from the glare).
What could be done instead? One interesting application I have seen is LEDs installed on the underside of a handrail. Unfortunately, I don't have any photos of a really good execution of this. Here is an example of an attempt that didn't quite work out:
It's better than the example above, but is still a problem, because it's still too bright near the lamps. What pedestrians need is accent illumination that helps them separate the stairs from the surroundings. When you have most of the scene lit with ~0.1 lux from skyglow and other distant light sources, and you then put 50 lux directly under the handrail, you've now created a 500:1 contrast. Your visual system doesn't deal well with that level of contrast, and it makes it harder to see.
For areas that are not brightly lit, moonlight provides a good benchmark. A typical full moon night is around 0.1-0.2 lux, so if you're illuminating a fairly light concrete, you really shouldn't need any more than that.
Update (October 20, 2021)
I found a great example, also in Potsdam. Check out the lights at the front steps of the Ernst von Bermann Clinikum (hospital):
The photo doesn't do it justice. It's a beautiful installation, there is absolutely no glare, it's not too bright, the color is warm, and in real life the area between the stairs is also sufficiently illuminated by light from the surroundings. I hope I get a chance to return to these two locations with a luxmeter and a DSLR camera sometime soon to do a more proper comparison.