Top floors in 5 story walkups are definitely cheaper in NYC this minute.

Apart from the stairs being a pain, your water pressure is also weak.

Is it? I lived in the 13th floor of a communism-era building my whole childhood and it was completely OK. Are US standards different than European?

Water will never make it up to the 13th story of a building just with the pressure from the water mains, so those building will need to do something to increase pressure on higher floors.

In a five story building, the water can get that high just with pressure from the mains, though the pressure will be much weaker than on lower floors, so the building doesn't need to have any mechanism for increasing the pressure. It probably wouldn't be done for newer buildings, but when the older walk-ups were constructed it would have been considered acceptable as a way of keeping costs lower.

NYC municipal water pressure is guaranteed to (I believe) the 6th floor. They may do better than that depending on the elevation of the neighborhood. Any higher than that, and the building needs to have a water tank on the roof or a high floor.

My understanding is that this was fairly standard in tall buildings everywhere.

Upper floor apartments were cheaper because they were meant for working-class people. The ground level and first floor were for shops and shopkeepers. The 2nd floor (that would be the 3rd flood in American terms) was the "noble" floor for rich people, with high ceilings and big balconies. The last floor under the roof was for housekeepers and cooks of the rich people below.

Obviously there were no elevators.

Well, I think the causality is the other way. The builders had good reason not to build giant penthouse apartments with views at the top: they knew their customers' preferences!