So you are anti H1B ? another tangent :D
As a results rates can't rise very quickly, which means that trucking companies can't really afford to pay drivers any better (obviously with some and slight exceptions, and only talking about US long haul trucking).
Trucking companies could solve some of their work environment related employee retention problems for free. For example by firing toxic managers, and treating drivers with a little more respect.
If so, it should be pretty straightforward - even with current rules - to have the human sleep (or watch movies) while the computer does the long-distance runs, then have the human do the last mile and exception-handling locally (not talking about split-second emergency takeover, just "the truck has stopped because it can't figure out what to do").
There is a difference between "can" and "does it help re: times" - and the answer at least for Europe is no (https://de.wikipedia.org/wiki/Lenk-_und_Ruhezeiten). The "down time" has to be in a stationary vehicle or outside of the vehicle (e.g. hotel) in order to count.