If you do what you suggest, the following program crashes (and is well
typed *)

exception Found of 'a;;

let rec assoc_exn n = function
  [] -> raise Not_found
| ((x,y)::l) -> 
  if x = n then raise Found y else assoc_exn n l

try
  assoc_exn 1 [1,2]
with 
  Found x -> print_string x (* x will be an integer, not a string *)