When we venture into the wilderness, we bury our solid human waste (or may even have to pack it out in some places). The basic guideline is to not leave faeces anywhere where it can be discovered or uncovered in the future. Yet along the popular North Kaibab, South Kaibab, and Bright Angel trails in Grand Canyon National Park, pack animals walk down the trail and up again, while the animals (which are non-native) leave their solid waste in the middle of the trail. As a hiker, I find this a very unpleasant experience, in particular when I'm tired and hot heading for the rim in the afternoon. Why are the outfitters operating the pack animals permitted to leave the trail in such an unpleasant state, when the rest of us are doing our best to leave no trace? Some sort of diapers (as in, any piece of cloth that would hold the solid waste for disposal elsewhere) might work, or at least a stick and flick method to move the manure off-trail?
Unlike human visitors, Equines (horses, mules, and burros) must have their feet cleaned and be on a special diet several days prior to venturing on to the trails.
Feed: Clean trailers, hooves, coat, mane, and tails prior to entering the park. Feed stock weed-free forage or processed feed a few days before the trip. To prevent introducing non-native plants in the park, use only certified weed-free forage— hay, straw, and mulch. Proof of certification tags required. Forage may not be taken beyond trailheads. Use pelletized feed, hay cubes, and grain products in the backcountry. Do not leave feed on the ground; use a feedbag or tarp. Pack out unused feed. Grazing not permitted. Source
Additionally Equines are only allowed on specific trails.
I could not find any requirements for people to have clean shoes nor modify their diet prior traveling the trails.
You are comparing apples to oranges, unless you happen to be vegan on a certified weed-free diet, without bowel control.
Edit I have been searching for officail documentation about cleaning up mule droppings. I have not found anything that specifically says what the clean-up expectations are.
It looks like the trails you mention are corridor trails
A corridor trail receives the highest hiking and stock use by visitors to the park and mule use by park concessionaires. To accommodate this, the National Park Service regularly patrols and maintains corridor trails.
This would imply that the droppings are cleared regularly but not necessarily at the time of deposit. It seems reasonable that some clean-up occurs, as without some removal there would more than you describe. This clean-up would be more likely off peak tourist times.
References for cleanup: (from comments provided by Jan Doggen)
Xanterra has a small crew that attempts to clean up mule waste on the trail.
Lately, they've been spending more time rebuilding trails than shoveling droppings. Source
Each year, the park receives numerous complaints regarding trail conditions and mule waste on the trails. Source
Ok the confusing term here I think is diaper. Which for me translates to nappy. Which means big nasty plastic lined item.
If you're referring to Manure catchers, these are items designed to short term hold some horse waste - think carriage horses on a wedding carriage and you don't want the waste dropping to spoil pictures etc. Or horses being used on busy streets. They're really for use in towns and cities. From experience on a two hour trek my horse could go at least twice, trekking on main roads and fields most people get used to seeing muck on roads around a horse yard.
Often these are made from plastic or vinyl with leather straps, which clip onto the saddle. So in doing this there may be requirements to changing existing gear.
They can be rather difficult to use based on the fact you have a lot of additional straps, and they tend to hold one poop at a time, so based on the above you'd be looking at a possible 1 stop to empty per mule per hour. Not all horses like items around their tail either (you can get saddle hooks that stop a saddle sliding forward on a horse with shallow withers) so bare the creatures comfort into consideration as well.
All in assuming they have a number of creatures, using these could add considerable time to their treks. They would need to be regularly emptied which would take time. Also consider that horses wee a couple of gallons at a time, so leave a big puddles where they go, we can't and shouldn't try and hold this.
Essentially equine waste is great for the earth, it's a fertiliser. Like any animal waste you find on a trail, horse, dog, fox, rabbit - it's poop and it will go away. As stated by @JamesJenkins in his brilliant answer the diet they have is different to humans. Plus there is no guarantee it would collect everything. It's probably be more cost effective to buy a shovel, or a manure scoop and rake, which can move manure easily and pop it off the main trail.
Good answers here already. I would add that based on my conversations with rangers, one of the main reasons waste from humans and from animals like dogs needs to be buried/removed is due to the impact of the scent on the wildlife. Humans and dogs both have a "predator" scent which can cause wildlife to avoid an area with feces from these species. As a "prey" animal, horse and mule manure will not have this same impact on the native animals in the ecosystem.
Between the logistical reasons listed in other answers and the reduced impact due to diet and the non-predatory nature of the animals, manure from stock can generally be left behind with minor impact on the environment. In other words, the unpleasantness for you as a hiker is probably significantly greater than the impact on the ecosystem.