Yes, overload is real, you can never eliminate crosstalk only suppress it, and degenerate cases will probably pop up as the tehcnology scales. But coming to a compromise that allows every car to generate a map of the road should easily be possible. Well, "easily" in the technological sense, perhaps not the political sense.

For military applications it's more useful to have one radar at high range/power than to have n radars at low range/power, while it's just the opposite for civilian lidar applications. So I don't see military radar SOP as evidence that this is inherently difficult.