My stairs don't have a visible ledge. I don't know why people are acting like that's standard. I think only one of the homes I've lived in has had a stairwell with ledges.

I guess I should address the "wear" on the carpet as well: it doesn't look worn to me, it looks disturbed. Like before this person tried shoving their mattress up the stairs and got it stuck, they carried a heavy dresser or or something up the stairs and dragged it up each stair, sliding it along the carpet. I suspect this is a person moving into a cheap efficiency apartment, since the one my father moved into last when he was still alive looked extremely similar.