Why it damages more than it stains
Fresh urine is mildly acidic and becomes strongly alkaline as it breaks down. That shift attacks the dye bonds in wool, which is why old urine spots on orientals often show as colour change rather than as a stain: a red that has gone orange, a blue turned grey, a defined pale patch. That damage is chemical and permanent. The odour is the secondary problem; the dye is the one that costs money.