This makes intuitive sense but is not borne out by research such as [1]. The < 20 mph scenario, one of traffic, consists mostly of stress and the general unpredictability and frustration of the whole scenario.
The problem of Level 3 autonomy is not cognitive load but the general lack of active feedback on the one hand, and a lack surprising events to mediate the allocation of attention on the other. It makes sense, the longer you're encountering non-events, the more difficult it will be to justify alertness. Surprise guides attention which in turn is strongly correlated with alertness. The longer one must remain alert, especially without surprise, feedback or reward, the higher the levels of subjective effort and mental fatigue.
Intuitively, if you imagine that only a few things are filtered to attention, the less surprises, the more predictability, the more difficult it is to select what to attend to, the more likely your mind will begin to wander. This is one explanation for the finding in [1]:
The fact that the number of false alarms increased suggests
that the rather dramatic increase in missed targets was not
due to a simple reduction in the number of responses:
the number of responses to nontargets even increased.
This suggests that the observed deterioration of performance
is not caused by task disengagement but may result from increasing
difficulties for subjects to correctly identify targets
This is also related to the very complicated aspect of maintaining concentration over extended periods of time (you can play a complex but engaging game for longer than you can a dull monotonous task) and the explanatory failure of a resource depletion account. There is as yet no completely satisfactory account for why perceived fatigue occurs but all the best models have attention, motivation and reward in common.
[1] In the linked article they specifically call out driving as an activity sensitive to mental fatigue http://www.sciencedirect.com/science/article/pii/S0926641005...