Urine and poop are only a point source if you have your cows corralled in, such as in a feedlot. If you can get cows to use a 'bathroom' you can treat it as a point source even if you are free-ranging your cows.
This is only partly true. One of the problems with almost all cattle pastures, even those that do 100% pasture-raised beef, is that cattle are like all animals and they have habits and preferences, so they tend to congregate in the same areas day after day, nearby the watering tub or under the shade tree, which means their urine and poop are concentrated in small areas.
One Regenerative Farming's emphasis, widely practiced on many high-quality grassfarms across America, but pioneered on Kiwi sheep farms, is the regular, constant movement of cattle. Whereas most cattle operations in the USA have some kind of rotational grazing system, it tends to be larger pastures with the livestock inside for very long periods of time. What this causes is a large amount of waste of the animal byproducts--the pee and poop are concentrated and oxidized by the sun and wasted. What the Kiwis pioneered was using temporary electrical fencing and frequent movement of the animals, alongside "intensive pasture management" (the management is the intensive part--carefully monitoring the sward and keeping it at optimal growing height--grass growth rates follow a sigmoid function, so if you graze too low, it takes a long time to grow back, but if you graze to just above the peak growth height, it regenerates much more quickly), allows higher stocking rates, lower environment impact, increased carbon sequestration, and many further benefits.
It takes more labour. Sometimes you move the cows daily, occasionally twice a day, rather than once a month or whatever. But the impact on local ecology is fantastic. Plus, if you move chickens into the pasture after the cows, they help spread the manure, eat all the fly larvae out of the patties, and act as a natural antibiotic (who needs a depreciating piece of farm equipment to spread all that poop when you can use appreciating livestock?).
I wonder how rotation grazing plays with training them to go in a particular spot, though. Seems like it would be at cross purposes.
Definitely better if you can manage sheep cows and chickens on the same property, but that may still be beyond some people to manage. Just the fact of rotation would tend to mean that your cows are on average farther up in the watershed than they would be if they have the entire area to themselves all the time, for some of the reasons you already stated.
More ammo against feedlots is a good thing.