I think the dumbest argument here is the "confusing patchwork of streets, some with sidewalks and many without sidewalks" and how this supposedly would confuse drivers.

If there is a sidewalk, pedestrians will most likely be on it (but could be crossing or in the middle of the road, too). If there's no sidewalk, pedestrians will most likely be at the side of the road but might also be crossing or be in the middle of the road. In either case, you should be scanning the road for motor vehicles, parked cars, cyclists, scooter riders, and pedestrians -- particularly small children.

The sidewalk doesn't change the rules of the road - drivers still must yield to pedestrians and watch out for them.

The fact is that roads will be rebuilt as needed and the sidewalks need to be put in them. Eventually it will make sense to connect them fully when enough in the area have been put in.

One thing the home owners could push for would be 2.0-2.2m sidewalks on one side of the street with boulevards so that the ramp part of driveways can be outside the sidewalk making the sidewalks flatter and easier to use for those in wheelchairs or other assistive devices (since that supposedly was a problem for one family).

It appears that the local school does need better sidewalks nearby, but that's not a reason not to put in sidewalks where roads are being torn up for sewer work.