Dehydration is a common cause for cats to be ‘ill’ and brought to the vet,* so it could be that their piss reeks because they are having to concentrate it so much in the first place.

*source: a dimly remembered conversation with a vet friend when I asked her why she was adding water to the already wet food for her cat. She said her cat could never be encouraged to drink enough, so it was her way of staving off the annoyance of giving iv fluids to her own animal someday.