> The rudder is necessary for directional control specifically turns,
Only if you add a secondary constraint of coordinated turns, which are important for passenger comfort and efficiency, but not directly a safety concern. (You still need directional stability, but that's provided by the fixed portion of the vertical tail, not the rudder.)
> and for flying straight in a crosswind.
Only if you add a secondary constraint of alignment between body angle and flight path. This constraint is totally absent in normal flight -- it only comes up during takeoff and landing, where it's useful to have the plane lined up with the runway to avoid side-loading the landing gear. In the case of a known rudder failure, you'd head to an alternate where there's not much crosswind, to avoid this issue; but you wouldn't expect many issues getting there.
The third case where the rudder is actually critical is when combined with other failures, especially asymmetric engine failures. There are parts of the flight envelope where a single engine failure combined with a rudder failure would not be expected to be survivable.
In fact, the rudder does not do what new pilots think it does (it is NOT like a boat rudder at all, really, because the plane banks) that instructors will often make you practice flying without using the pedals at all.
Only if you add a secondary constraint of coordinated turns, which are important for passenger comfort and efficiency, but not directly a safety concern. (You still need directional stability, but that's provided by the fixed portion of the vertical tail, not the rudder.)
> and for flying straight in a crosswind.
Only if you add a secondary constraint of alignment between body angle and flight path. This constraint is totally absent in normal flight -- it only comes up during takeoff and landing, where it's useful to have the plane lined up with the runway to avoid side-loading the landing gear. In the case of a known rudder failure, you'd head to an alternate where there's not much crosswind, to avoid this issue; but you wouldn't expect many issues getting there.
The third case where the rudder is actually critical is when combined with other failures, especially asymmetric engine failures. There are parts of the flight envelope where a single engine failure combined with a rudder failure would not be expected to be survivable.