Isn't some simple mechanical fuse / switch sufficient for the airbag deployment system? Also, did old cars require SDM for the seatbelt to lock properly? Why are they changing mechanisms that have proved themselves?
Isn't a carburettor and magneto sufficient to run an engine? The answer is yes, if you have no regulations, reliability and/or liability to be concerned with.
Air bag systems have had software for literally decades, it's not new. Seatbelts still have mechanical locking. Electronically-controlled pre-tensioning is something else that has been around for decades now, and is part of the airbag control system.
Modern air bags have variable deployment energy, which requires determining the severity of the collision, the weight of the occupant, etc. There are also side curtain and many other types of airbag that should only deploy when required, so the pitch, roll, and yaw, and even sideslip of the vehicle has to be known. Side curtain airbags need to deploy before the vehicle lands on its side, so software is required to predict when impact is likely to occur.
Also, electromechanical systems can't self-check and diagnose themselves when there is a system failure. Air bag systems continuously monitor even the resistance of the igniter in the airbag to make sure it is correct.
As vehicle manufacturers found out with carburettors and emissions regulations, mechanical systems quickly become too complex and unreliable to react to many inputs. There is no new passenger vehicle sold in North America that doesn't run its engine entirely from a computer. It's just that superior. Likewise with airbags.