Increasing road capacity can cut commute times, for like a week. When people know they can get somewhere more quickly and more reliably because of increase road capacity, they drive more, which in aggregate, causes the new roads to become as gridlocked as the old roads, and the old roads are still gridlocked.
Single occupancy vehicles are just not efficient for moving large numbers of people around. In order of preference you basically want people to 1. not have to commute (telecommute) 2. walk 3. ride a light vehicle (bike, electric scooter, whatever) 4. take a train or Ferry 5. take a shuttle 6. take a bus 7. carpool 8. drive 9. take a plane.
(Actually not sure where Lyft and Uber fall in that stack given there's evidence that ridesharing platforms seem to be increasing traffic in the areas they operate in.)
Of course you can mix any and all of those but your city's transportation infrastructure ought to accommodate each of them and prioritize each in kind.