"a safer reaction to overspeed would be to apply speedbrakes/reduce thrust, instead of raising the aircraft's nose"
In most airliners they are not speedbrakes, but spoilers. Fighters generally have speedbrakes. Spoilers reduce lift as well as increase drag. Hence in airliners they are generally only used on descent when reduction in lift is required and not in level cruise or climb as they reduce stall margins. In the rare event of an overspeed trend in level flight at altitude, you reduce thrust first and only then consider using spoilers. This was not an overspeed situation but a nose up pitch with reducing airspeed.