Because A City Besieged says, "Choose and discard 1 location... controlled by each player", can its effect still be used if there isn't a valid location controlled by every player? I know there are different rulings with regard to each player doing something and resolving an effect as much as possible.

This is a passive effect, so you do as much as you can, including choosing targets. That's why Marched to the Wall is a common opener for Knights of the Hollow Hill.

Wow I never realized how bad this templating is. That is some epic fail placement on "if able". It basically reads that if you can't choose them all, you can't choose any.

It is currently interpreted and played as:

"When revealed, for each player, choose 1 location with printed cost X or lower controlled by that player, if able. Discard all chosen locations from play. X is the number of City plots in your used pile."