A Boeing airliner has a travel limiter on the control surfaces that is automatically adjusted based on the speed. Exceeding that travel puts enough torque on the airplane to literally tear the structure apart.
There was an Airbus incident years ago where the pilot stamped on the rudder pedals to violently move the rudder full travel lock to lock, and it tore the rudder vertical stabilizer off.
There are also situations where no amount of control input is going to wrest control back from an uncontrolled dive.
In other words, designing the "feel forces" and travel has a large number of variables to it, and is not simple at all to get right.
For a dive fast enough, you run into an effect called "separation". This is where the air flowing over the wing no longer converges at the trailing edge, but separates. This separation can engulf the elevators such that even at full travel, the elevators are operating in dead air and from then on, you're just along for the ride into a crash.
This is a problem for many, many aircraft designs. You always gotta watch your airspeed.
This happened to a 727 once, where the autopilot went berserk and sent the airplane in a dive so bad that separation happened. The quick thinking pilot decided to lower the landing gear in a desperate attempt to slow the airplane down. He succeeded, although the slipstream tore the doors off and bent the gear backwards, and saved everyone.
It also happened to a 707, where the pilots weren't paying attention and the airplane slipped into a dive. By the pilots realized what had happened, they no longer had pitch control. One of them desperately began cranking the trim wheel by hand, and they managed to pull it up just before it hit the ocean.
Yeager's X1 rocket aircraft had this problem, as did the F-86 jet fighter.
For another fun anecdote, the F-80 Shooting Star had a problem in that its engine was too powerful. If you oversped the airplane, it would go unstable and pitch up, tearing the wings off. That meant the pilot always had to have one eye on the airspeed (yes, my dad was an F-80 pilot, and flew them in combat). One day, a pilot had a Mig on his tail he couldn't shake. He thought, I'm dead anyway, let's see if I can pitch up and lose the Mig. So he firewalled the throttle, and sure enough the F-80 went through a violent maneuver and miraculously the wings stayed on and he shook the Mig off his tail. When he landed, the wings were bent up and the airplane was scrapped.
Dive bombers used "dive brakes" to keep from overspeeding the airplane. My dad's favorite method for attacking an anti-aircraft gun emplacement was to dive straight down on it. AA gunners did not want to fire vertically (think about it). But it required my dad to have one eye on the target, one eye on the airspeed, and his third eye on the altitude.