One more try here. We have a 100m race. Average high school track athlete vs an Olympic gold medalist.
The Olympic gold medalist has to run through waist deep water. The high school athlete runs downhill through air.
Who do you bet on?
Now, if both were smart enough to stay out of the water, a more interesting race would be the Olympic runner uphill vs the high school runner downhill.
It would look pretty stupid to hold the race in water, up or down hill.
The difference with aircraft is that sink from loss of lift causes the relative wind to create an even higher AoA. This is why it is imperative to drop the nose faster than sink increases AoA, preferably at the pre-stall warning.
Some simple math can show an airliner falling at 200 knots can "power" up to 500 knots and still be stalled. From 30,000 feet that's around 100 seconds to impact. Making matters worse, now you risk V never exceed as you finally come to your senses and pitch down to unstall.
the physics of turning favor lower speed. Unstall first, then add power.
Essentially, it becomes a question of knowing the performance limits of the aircraft. As engines are generally at or near full power in a climb, the risks of continuing to climb in a stalled condition become obvious.
Can it be done? With hovering capacity, yes. Sustained climb while stalled? Slowly, yes. Economicly? No.
Most aircraft will lose significant airspeed well before 45 degrees climb angle. Even the Olympic runner cannot maintain speed on a steep grade. To get a better feel for this, draw some closed vector diagrams for various climb angles. The gap between winged flight power requirement and hovering flight power requirement is simply too great for most aircraft to simply "gun it" while ignoring aerodynamics.