Current charge times make "recharge when the driver stops for breaks" impossible.
Not really, no. Current charge rates mean you can get about 100 miles of range in 20 minutes on a standard DC charger. If you're a tesla owner that's more like 200 miles of range in 20 minutes.
Big rigs typically get in the range of 8-10mpg, so they're roughly 4 times less efficient than cars. That implies that you could get about 50 miles for 20 minutes of charging on a tech similar to tesla's. Big rig drivers are required to take 10 hours of break in every 21. That 10 hours is enough to add 1500 miles of range, 11 hours is enough to drive roughly 770 miles.
It seems like even with Tesla's current DC charging tech there's *more* than enough ability to charge a big rig for all its current driving time.