While I've seen the pants thing it doesn't seem to be quite as bad as you present it. What I've always seen is not directly on the path--say, on the ground around a tree, or in the gutter etc.
The reality is that there aren't enough public toilets for a small kid to be able to reliably hold it until one can be found.
I definitely understand the bit about queues. It's nuts and it can be a problem when I'm out with my wife--I'm usually carrying stuff and that limits my ability to keep up in the crush. (Because of the bulk, not the weight.)