The PH of your urine can vary. Urine is also not sterile, so you are introducing waste products, bacteria, and salts directly into your skin holes. The urea concentration isn't especially high at 2%, compared with topical solutions that start at 5%. CeraVe and Eucarin both have a product with urea in them.

You are right, in that urea does break down into ammonia. So aged urine was used to tan hides, since the ammonia would break down the leftover fatty tissue/grease, and loosen all the hair and fibers.