Why not km/liter, which is a much more convenient format for any sort of day-to-day use ...

It does not really matter. There are three situations where you will ever need the fuel consumption stats, and in each one of them both ways are just as easy to use. I used MPG instead of km/liter below, since the two are conceptually equal, but the former makes for easier reading as it is a commonly used unit.

1. Comparing the fuel economy of cars

bigger MPG is better

smaller liters/100km is better

2. Computing the fuel costs for a given trip, when you cannot use the "top up before you leave, top up again at destination" method

divide the trip length by MPG to get gallons

multiply the trip length by liters/100km to get liters

3. Estimating whether you can reach a destination without refueling. This is the only case which you'll typically have to do in your head, since you are driving. Therefore you want to avoid division, which is difficult to do this way. However, both systems will cope easily:

multiply remaining fuel by MPG to get your range, and compare with remaining distance

multiply remaining distance by liters/100km (division by 100 is easy) to get required fuel, and compare with remaining fuel.

In the third situation both methods involve only a multiplication of two small numbers, so even if you cannot calculate the correct figures, it's easy enough to hit the correct ballpark with either method.

There does not seem to be a real difference between the convenience of the systems in day-to-day use.