I think planes can still fly with the rudder loose? If the bolt falls out and it loses control, wind will push it into the neutral position and then flying will still be possible with other control surfaces? But I guess if the pilots don't know and it happens suddenly at a critical moment or if the bolt causes the rudder to get jammed, then that would be really bad. But I assume it falling out would result in the rudder loosely returning to neutral...
Planes can fly with the rudder inoperable, although with some restrictions -- you wouldn't want to do a serious crosswind landing, and you wouldn't want to stack it up with other failures, especially asymmetric engine failures.
However, that doesn't mean that planes can fly with the rudder /loose/. A significant risk in higher-speed airplane designs is that of aerodynamic flutter, where aerodynamic forces excite a vibration mode in the airframe, or a subset of it. You can find some impressive video of e.g. bending modes in sailplane wings being excited, with increasing magnitude bending until the wings are destroyed (or the excitation is reduced dramatically, or shifted to a different frequency). While aeroelastic modes get a lot of attention in flutter analysis, loose control surfaces can be much, much worse, because movement of the surface within the lash provided by the loose connections is effectively undamped.
The rudder is necessary for directional control specifically turns, and for flying straight in a crosswind.
I've heard of a few cases where applying more/less power on the right/left engines can sort of crudely achieve the same thing, and you might get lucky and get on the groud without crashing, but loss of the rudder would be a serious emergency indeed.
> 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.
