Yes, drastically. But with it you bring new fears of how that data will be used by the government. You could also achieve something similar by forcing all vehicles to have embedded sensors that real time share data.
Are there any active research exploring this path? E.g. have cars to report about themselves or have a centralized control system (similar to air traffic control?)
Cooperative strategies open up a lot of new attack vectors. I don't trust those companies to design systems robust enough, especially if they'd have to build a standard together with competitors.
And in the end, your car has to be able to come to a safe stop and avoid dangers no matter the situation. Even with no other cars around or communication interrupted. To reliably achieve this will probably get you most of the way to "real" self driving, with humans/remote operators manually taking care of the few remaining cases.