The benefit of faster speeds isn't driver convenience, it's that you get cars off the road quicker for a given travel distance. Each city has a carrying capacity for the number of cars that may be on its roads at once, which is determined by the length of the road network and number of lanes. They also have a certain number of trips generated, which is determined by population. The number of cars on the road = trips generated * average travel time per trip. When that exceeds the carrying capacity of the city, average travel time increases, which causes a cascading effect that eventually results in gridlock.

The same effect plays out locally, on each individual stretch of road. When integral(# of incoming cars - # of outgoing cars, time) > carrying capacity of road, the road backs up, which increases the time required to traverse it, which further exacerbates the backup. This is why multi-lane arterials can reduce congestion; they can move a lot of cars off a given stretch in a short period of time, and provide a linear buffer where momentary oversupplies can collect without backing up the previous intersection.

You can also see this effect by looking at traffic maps of say, SF (grid layout) vs. Sunnyvale (arterial/collector):

https://www.google.com/maps/@37.7811106,-122.4106957,16z/dat...

https://www.google.com/maps/@37.3724565,-122.0375532,15z/dat...

Both of them have shitty traffic, but in SF the traffic spills away from Market street onto many of the side streets, such that no matter where you go it'll be gridlock. In Sunnyvale, much of the traffic is confined to major arterials like El Camino or Matilda, which are slow but still move, and side-streets that parallel them are often relatively clear.