Normally all those things you said would result in accidents. If the simulators randomly added delays for cars braking or starting up, and then kept a death count, it would be more accurate...
The bigger problem was that this type of behavior was the norm to the point where at slow speed intersections with stoplights (e.g. city streets around college campuses), only a single digit number of cars would be able to go through per green light.
Indeed, the most influential slider in the simulation seems to be the “max acceleration” one... if people accelerate quickly up to their max speed it seems to prevent traffic waves from propagating backwards. It meshes well with my observations 213929387 years ago when I used to drive in traffic.
So you would have various transition probabilities of a car driver moving from an attentive state into various inattentive states, with drivers having different reactions in each state.
It would also help to have a level of "variance" in individual drivers. So instead of having a bunch of drivers who are just as likely to make mistakes, you have some who transition far more easily into inattentiveness and some whose likelihood of damage/nuisance is higher than the standard driver when inattentive.
It seems entirely doable. (famous last words)
Where are you seeing this?