wouldn't this kind of be recycling the same piss time and time again?
Not "the same" piss. It's stuff your body produced to benefit you that was
supposed to be cycled back through (re-consumed).
At some point your body momentarily produces exactly what it needs to thrive, in excess, but doesn't
continue producing it indefinately. So, that particular combination that will make you thrive passes through at single moments, and since it is momentarily in excess, the body can't use all of it at that moment. The problem with throwing the urine away is that the body could use them in following moments.

Follow me...
Textbooks continually make a false statement time and time and time again. It is this one: "the kidneys filter waste." FALSE.
The kidneys filter excess ingredients and excess fluids, NOT "waste."
Where the actual waste is fliltered is in the LIVER. The blood, filled with nutrients, goes through the liver, that's where toxins are removed and eventually leave the body via feces. The only thing that makes its way to the kidneys is a purified form of blood, CLEAN blood. This cleaned blood goes into the kidneys then goes through the nephron tubule system then pressure squeezes it out.
WHAT THE FILTERING PROCESS IN THE KIDNEYS DOES IS
1) REMOVE EXCESS WATER, AND
2) THE INGREDIENTS THE BODY DOESN'T NEED AT THE MOMENT.
The excess water and ingredients become the urine. The nephron then reabsorbs some of the ingredients and those go into the bloodstream, but the remainder, which you will still need in following moments, goes out from the kidneys into the bladder and we piss it out.
MISTAKE: we flush these ingredients, yet we will still need them.
[The kidneys keep the elements in your blood balanced AT THE MOMENT IN TIME. The ingredients you don't need at that moment become urine. These elements are supposed to be cycled back through the body because you will still need them in following moments.]