Implications of the Existence of halts?

If halts? were to exist, then it could be used to solve problems that mathematicians have not been able to solve. For example:

Q: Are there any odd perfect numbers?

If there are any, then the following procedure would eventually find it and halt:

     (define find-perfect-odd           
       (lambda (n)  ; start n at 1 
         (if (perfect? n)                  
             n                             
             (find-perfect-odd (+ n 2)))))
Since there may not be enough time left in the universe to wait, we could ask:
     (halts? find-perfect-odd) ⇒ <the magic answer>
While halts? sounds too good to be true, this is not a proof that it doesn't exist.