Well if you take the cable off you should be able to get a much wider tire on.
No. The quick release on the cantilever brakes is open. The brake pads hit the seatstays. There is no taking the cable off. Cable travel or slack in the cable is not a factor. The brake is as wide as it can be because the brake blocks are hitting the seatstays. The only way to get the brakes wider is to take them out of the cantilever posts and release the cable from the brake. I doubt many people would want to do that every time they remove the rear wheel.
When we run wider tires on our tandem we have to deflate them a bit to get them through the brake pads. A bit of a pain, but not too big of a deal, and a lot easier than removing brake pads!
The only really annoying thing is when you get a flat, remove the wheel easily, fix it and pump it back up, and then remember that the tire won't fit through inflated. So then you deflate, install, and repump. Sigh.