I would be fine with assigned lanes with everyone keep-to-the-right (or left if you are in a country that leans that way). I usually stick to the right even when there is plenty of room to move if someone is on the wrong side. They usually figure out to get on their side of the walk by the time we meet.
However the city I live in is laid out rather dumbly with every store putting tones of shit all over the too-narrow sidewalk, or those trap door to the basement things that are corroded and look dangerous to step on. You are lucky to have a single lane to get past.
In that situation I am totally good with taking turns as long as everyone is keeping their head up and paying attention. If some douche is going to stick his head in his phone while moving through the one-lane section... he might get introduced to mister shoulder. Catch them in the arm, makes it more plausible you did it on accident, and more likely to knock the phone out of his hand.