Keyless pushbutton ignition replaces this problem with other problems - notably that the means by which the engine can be switched off in a panic-emergency (see above-mentioned Toyota runaway incident) by a driver who hasn't read and memorised the 700 page instruction manual isn't the same as in the cars (with keyed ignition) that the driver probably took driving instruction in and has potentially been driving for decades. With a normal keyed switch, you switch it off. With a pushbutton, what do you do?
A momentary prod at the on/off button? If you, as the auto manufacturer, accept a momentary prod at the on/off button as an instruction to turn the engine and entire powertrain off while driving, what happens when someone accidentally prods the button momentarily?
Hold it down for 3 seconds? A lot of them are like that. If the driver is in a panic and wants to turn the engine off, 3 seconds is an awful long time when the car is accelerating towards the back of a transport truck in front of you.
A very small number of manufacturers have gotten what I think is the right approach. Keyless, but not a pushbutton. A rotary switch in the same place where every other car has its keyed ignition rotary switch, and with the same switch positions. Want to turn the engine off? Same action as in every other car.
Both late model vehicles in my driveway have a plain ordinary keyed ignition switch, and I am fine with that.
The other problem that GM ran into is one that is unrelated to the type of ignition switch. What do you do with the car's safety-related systems (including, nowadays, electric power steering, ABS, and the airbag system) when the driver switches the ignition off (by whatever means, whether deliberate or accidental)? In the old days, that ignition switch simply cut power to (almost) everything. No more engine, but now, no more ABS, electric power steering, or airbags. Now one needs to switch off the engine immediately, but keep the safety-related systems running as long as the vehicle has non-zero indications from its wheel speed sensors, and *then* turn them off.
The GM cars that were affected by this had a traditional ignition switch that cut power to everything (except possibly headlights) - which has been the way it was since the beginning of having ignition switches. The consequence that evidently nobody had thought through at the time, is that accidentally bumping the ignition switch off while driving, disabled the engine, which disabled power steering, which made the car hard to steer (not impossible, but hard enough that someone not expecting it, and someone not used to applying serious muscle to the steering, would be caught off guard), which led to the car leaving the road and hitting solid objects with the airbags disabled because the ignition was off.
The law of unintended consequences, is inescapable.