Can think of two potential legal issues (to address the OP's question) other than required stops: following distance and lack of single file.

In a single paceline the lead rider will, after his pull, drop off to the side and drop back to the rear position, perhaps every few minutes. In Michigan it is not illegal to ride side-by-side, though IMO it is not generally a good idea due to potentially impeding the flow of traffic. I can't really say about other states. Probably one should consult Bob Mionske's book and see what his "national model" says, though it doesn't reflect the particular legal distinctions for all 50 states.

For following distance, we are tailgating. While for cars it may or may not be strictly illegal, it is not regarded as safe for non-interactive vehicles.

New technology may change that for cars, in the form of an automotive device called interactive adaptive cruise control. Adaptive cruise control uses forward-looking radar or lidar to detect the distance to the car ahead, and can automatically control the throttle to follow the car ahead at a generally safe distance. The interactive system can allow a stream of vehicles to react as a unit, forming a string of cars (called a "platoon") that draft each other. Following distances, about a car's length at highway speeds, are regulated electronically, ensuring the constant active control that would be needed. The benefits are that many more cars can transport on a given highway due to greater road occupancy, and (as in bikes) much better energy efficiency for those vehicles.

But due to fleet legacy issues, it might be 50 years before platooning is common in cars.

Despite the digression, I'm not sure single pacelines are illegal, though lengthy digressions soon may be.