You are absolutely correct that things can go wrong very quickly, especially at altitude. Modern planes fly very high for reasons of efficiency, but as the air thins, the window between stall speed and overspeed becomes narrower[0]. That's why piloting always emphasises the need to be thinking ahead of what the plane is doing and not following it.
For this incident, they were flying at FL350 (35,000 feet) and had a service ceiling of FL370 at their current weight -- that's a difference of only 2,000 feet. Within 30 seconds of the autopilot disconnecting, Bonin put the aircraft into a 7,000 feet/minute climb! So that margin was eaten up very very quickly.
If you're interested in aircraft incidents and accidents I recommend Petter Hörnfeldt's excellent YouTube channel Mentour Pilot[1]. He goes into deep technical detail and has covered not just AF447 but many other incidents where the pilot lost situational awareness and put a perfectly working plane into the ground.
[0] https://www.boldmethod.com/learn-to-fly/aerodynamics/coffin-...
[1] https://www.youtube.com/@MentourPilot