There are many loads where that system would create a lot of inefficiecies. The type of loads where it makes sense are already run that way. It's called LTL (less than truckload) and is one of the most volatile sectors of the industry. Wages tend to be higher in that sector, though, and there's more home time, so they tend to go to more experienced drivers with excellent driving records.
Yes, overworking drivers is more "efficient". Right now, the labor market won't let employers do that. The winners will now be the employers who figure out how to give their truckers a better life without wasting too much time sitting around at crew change points.
Or buy a semi-autonomous truck that can be used in convoy mode - one driver in the lead, two trucks behind following. Once it gets to a city they all get drivers to navigate to the depot. This is already a feature of the Tesla Semi.
Now that's a good point. The job could be much better if the employers were better organized. Employers want to send someone out on the road for weeks at a time. With better scheduling, the first driver drives for four hours, stops at a truck stop, and swaps trucks with another driver going the other way. Both drivers end up back home at the end of their shift. Where's that Flexport guy who's always on here when you need him?