I can think of a number of ways in which dwarven and animal excrement could add some new !!Excitement!! to the game.
1) A novel projectile material for the catapult. Nothing voices your disdain for elven merchants and goblin siegers like flying poo being hurled at them at terminal velocities.
2) Something that is less likely to cause serious crop problems than raw potash as a fertilizer. (bonus if toady puts in actual C:N:P ratios for crops. Potash only supplies P. Bloodmeal supplies mostly N. Poo supplies C, P and N.)
3) Something for potash makers and wood burners to actually do. (Poo can be burned for potash, and also turned into charcoal.)
4) while disgusting, urine was fundamentally necessary to medieval textile and dye processes. Specifically, for the rhetting of linen, and the setting of blue dyes. (Woad and indigo blue are really the same pigment, and require ammonia to dissolve in the dyebath. This means festering urine is required.)
here are some authentic dye recipies from the medieval period, involving urine, for your viewing displeasure.
Genua Madder Red.
TAKE three Pound of Allom, one Pound and half of Tartar, boil the Stuff in it an hour and a half, then pour off the Water and put fresh Water into the Kettle; make a Liquor of ten Pound of Madder, four Ounces of Pot ashes, and some Urine, and boil it off when it hath dissolved one Night.
Ox-blood Colour.
FIRST Tinge the Stuffs Yellow, with a quartern and half of Madder to a Pound of Goods, Allom and work them till they are sufficiently beautiful, then rince them well out, and put into the Kettle a Tub of stale Urine, and boil it again till they take the Dye; then roll the Stuffs three or four times through it; and rince them very clean.
Another sort of English Red which is deeper.
BOIL your Ware to be Dyed, with two Ounces of Allom, two Ounces of Tartar, two Ounces of Aquafortis, tempered with two Ounces of fine Tin, a quarter of a Pound of Madder; this is the proportion to one Pound of Wool or Stuff, and ought to be augmented in proportion to the weight of the Cloath, only the quantity of Tin must not be more than doubled to twenty Pound of Ware, for a large quantity of Aquafortis may be as well tempered with two Ounces, as with a quarter of a Pound: Then boil the Cloath two Hours in it, stirring it as much as is proper, cool it in the Suds and rince it out. And to Finish the Dye, for every Pound of Ware, take a quarter of a Pound of Madder, or 1/2 a 1/4 of a Pound, according as you would have the Dye deep, a 1/4 of a Pound of blew Wood, 1/2 an Ounce of Allom. Stir the Cloath very well in it, and when you find it takes the Dye, add half an Ounce of purified Pot-ashes, and stir the Stuff well about that it do not spot, This Dye appears very beautiful to the Eye, but all the Wood Dyes are apt to stain very much, not only by Wine, Urine, Vinegar; but by dirt, foul water, &c.
Straw Colour.
THE Ware being first Dyed Yellow, throw into the Dye half a Pint of Urine, put it in, and Work it about as long as you think convenient.
How to Dye Woollen, Silk, Worsted or Yarn of a Flesh Colour.
PREPARE two Pails full of sharp Lye, from a Handful of Beech Ashes twice boiled; into one of the Pails, throw one Pound of Potashes, and heat the Lye in a brass Kettle, and when the Pot ashes are dissolved, stir the Liquor very well; stir up the Fire, and then put in one Pound of Flocks or Shreds of Madder Red dyed Cloath, hang it over the Fire, let it boil sometime, and stir it about with a Wooden Instrument; then fill it up with the remaining Lye made boiling hot, always taking care to keep it boiling and stirring, and a full hour after fill it up again with Lye, then scum it clear, and as it boils away for three hours, fill it up with stale Urine: all which being carefully done, pass a thread of Yarn through it, and Draw it through your Finger; to examine whether there is any Hair hangs to it, and if it doth, put in one quarter Ounce of Pulverized Turmerick, stir it about very well, and try with the Yarn Thread again, whether it takes as good a red as you desire. If you would Dye your Ware of a beautiful orange Colour, then pour half your Dye into another Fat, put into it your Ware, Dyed before yellow with Broom or Dyers Yellow Weed; and in the remaining part of the Dye, you may put your White Goods (which by the way must not be Allomed) covering it very close, that no Steem evaporate till it be cold: Then throw about two Pails full of Spring Water into a Tub, and rince both your Colours very well therein, dry and Press them, and then rince them again in Spring Water. If you would have a very Beautiful Flesh Colour, hand your Kettle (which must be of Brass) again over the Fire, boil the Dye to Suds, and put in your Ware, leaving it there till it be cold, then rince it in the same Water, which you have before, but remember to take especial Care, that you do not mix the Orange and Flesh Colours together.
*as you can see, stale urine was an indispensable product of the dye industry.
5) a more accurate view into medieval leather and tanning industries....
6) Yet another means of syndrome spread within a fortress, and another source of micromanagement FUN. Possibly with explosive/flammable gasses! (flaming gas trap! WHEE!)
Instead of fixating on how Poo and urine are "Gross, eww. I dont wanna play with that!", think about how those items are insanely useful, and even indispensable.
It isn't about "Dwarves going off on potty breaks"-- its about the "Oh, I fling PIGSHIT at you! Your' mother was a hamster, and your father smelled of elderberries!", the potential for exploding gasses, and even more micromanaged process flows, and even making currently useless dwarves into dwarves that are suddenly VERY useful.