Consider a long-running multi-delete operation that ends past the end of the logfile that we have (e.g. it ran for 24 hours on an active multi-TB collection). There would be no way to determine whether this op is running without analyzing db.currentOp() (which is not an easy task). And you also would need to know to look there.
A good option would be to log all long-running operations periodically, let's say each 10 minutes or so.