It is not unusual to seek the route in space that minimizes travel time, for example, a drive from point A to point B may go out of the way to include a high-speed facility that reduces travel time even if it increases distance traveled.
But what about routes in time? Does it ever make sense to minimize the distance traveled? Yes, for example, when a resource cost is related to the distance traveled, as with some taxi fares, or the wear on tires, or for railroad track access. In other cases, minimizing time and distance go together, as with the great circle routes of ships or aircraft.
A race could be delimited by an amount of time rather than a distance. The goal would be to maximize the distance traveled in a fixed time period, rather than to minimize the travel time over a fixed distance. For example, walk-a-thon participants may seek pledges of support for every mile they travel within a specified time period.
An indirect example would be those sports that take place over a fixed time period, such as basketball, football, and hockey: the goal is to score the most points, which usually involves moving the ball or puck the greatest distance (though there are strategies to control the ball and run out the clock).
Commuters seek to minimize the travel time rather than the distance traveled, so a map with distances is not as important as a map with travel times during rush hour. There are apps that show (or speak) the route with the shortest time. Restaurants near businesses need to take the fixed lunch hours of their potential customers into account; short travel time routes may lead through walkways, highways, or public transit stops.
In all these cases, the route through time is more important than the route through space.