On many aircraft you do get extra warning. The Lear 40/45 gives you:
- Amber CABIN ALTITUDE at 8750'
- EMER PRESS kicks in at 9500'
- Red CABIN ALTITUDE plus the voice finally at 10,000'
Obviously if it's catastrophic, all those will go at once, but hopefully the amber warning will give you a chance to get the mask on before starting the dive of doom.