What you're missing is that CGP Gray is making that video in the context of real life Western society, where individual vehicle ownership is very high, mass transit utilization is very low, and people still live in big sprawling suburbs in the US.
GDI does not have this society; life in GDI is not identical to life in the 2020 West, or for that matter the 1995 West at the point of departure when tiberium first appeared.
While I'm sure there are still private individuals commuting to work in personal vehicles, there has been little or no manufacture of personal cars since 2047, and it is now 2057.
Car fleets are shrinking relative to the scale of the road network.
Buses and rail transit (with correspondingly lower accident injury rates per passenger-mile) are expanding relative to the scale of the working population.
Thus, the problem CGP Gray documents does not exist to the same extent in GDI's society, because of the ways GDI's society is different from real life.
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Therefore, the main impact of introducing self-driving vehicles is labor savings. Accident rates will have already been driven down dramatically by reduced traffic levels, and quite possibly also by safety innovations built into NON-self-driving cars such as collision warning systems. What will be impactful is the elimination of demand for individual drivers of vehicles... but this requires that the self-driving systems be capable of safely operating heavy machinery such as vans, buses, trucks, bulldozers, and so on.
Hence, this is likely to be a research project that frees up Labor in exchange for Capital Goods, not a project that frees up Logistics and Health in exchange for Capital Goods.