Why is urea not converted to ammonia in the body?
The answer to this question is quite simply this:


  The activation energy for the uncatalysed reaction is such that the
  amount of decomposition of urea in aqueous solution at blood temperature and
  pH is negligible in the time taken for the transfer of urea to the
  kidney.


The literature supporting this is very old, so I shall first cite a relatively recent (2004) and (I think) freely available paper by Robert P. Hausinger on urease in which he writes:


  The substrate [i.e. urea]  is highly resonance stabilized (30 to 40 kcal/mol), thus
  decreasing the reactivity of its carbonyl carbon so that spontaneous
  hydrolysis of urea has never been observed. Rather, urea decomposes
  in solution (with an estimated half-life of 3.6 years at 38°C) by
  the slow elimination of ammonia to form cyanic acid (17)


Reference [17] is a paper by Zerner in Bio-organic Chemistry from 1991 which requires a library subscription. In effect it quotes the same half-life:


  The urea molecule is very stable. Between pH 2 and pH 12, the
  nonenzymatic decomposition of urea in aqueous media is independent of
  pH and has a half-life of 3.6 years at 38°C (36-38).


References 36 is a book written in 1923, and references 37 and 38 date from 1942 and 1955, respectively. I have not checked the latter, but can if anyone demands it.

All of which is not surprising, as the purpose of the urea cycle in mammals (etc.) is to eliminate toxic ammonia, and, as @Fizz points out, the enzyme urease is needed by bacteria that utilize the compound.