It's a range of factors, closely related to what you've said, but about various pressures on the land.
One factor is that with one or more overnight stops you can penetrate far further into a protected area - day trippers are limited to a few hours' hike from the road; one night's camping doubles that. This means that if the area serves as a wilderness refuge for wildlife the daytime disturbance from overnight stays is far more significant. People are also more tolerant of other people during the day, so unrestricted will disperse at night, spreading their effect on the wildlife and ground. If you can only camp at certain locations, these will only be big enough for a certain number of tents, so how would you handle the situation where 10 tents turn up late at night for 5 spaces without a form of prebooking?
Overnight disturbance of wildlife is a further factor. Noise travels further at night, people use lights, they cook (and presumably need to protect their food from bears in your example location).
Trampling is probably not a big factor, but is quite different between hiking and pitching a tent. Humans are generally likely to leave far more of a trace if staying overnight: even people who are being careful are more likely to drop something in the dark, there's the need for the toilet as you say (and note that people camped near water may be unlikely to go far enough from camp in the dark to avoid polluting it).
Requiring a pass restricts access to those who plan in advance, and have, at some point, been presented with a list of rules that they have to agree to. This should correlate to some extent with those who are prepared to behave well.
In parts of the Scotland where roadside camping in motorhomes is allowed, some areas have had to bring in a permit system because of overcrowding causing erosion etc.; this also applies to tent camping (coincidentally I'm planning a cycling/wild-camping trip passing through this area).