Pros and cons of a output discharge of a power distribution switch
It's probably better to start with an example of what output discharge function can be used for.

Let's say you have a low-power transmitting circuit (eg. sending data to a receiver/reading device) powered by a 5V source. You added a bunch of decoupling capacitors close to the device to make sure the power is stable. Whenever this 5V power source is "turned-off" (eg. input power unplugged), its output decays slowly and it takes ~20ms to get from 5V to 3.3V because of all the capacitors on this rail needing to discharge through the different sink paths (here = your low-power transmitting circuit). If the working voltage range of the transmitting circuit is 3.3V to 5V, then it will still function even 20ms later, maybe even more. However the data it is transmitting is completely corrupted because the source IC of this data had "died" when voltage had reached 4.5V. For the sake of system stability, you don't want this to happen.

There are few ways to solve this, output discharge is one of them. If you had this distribution switch inline with your 5V rail and your transmitting circuit, you could make sure its own local 5V is "killed" rapidly after the power is unplugged relying on the output discharge circuit of the switch. You may even want to put both the data source IC and the transmitter on the same local 5V rail to guarantee a quick shutdown of both devices at the same time.

What could go wrong with output discharge? At worse, if not sized/implemented correctly and triggered for long period of time, you could burn off the discharge resistor.

Other than that it is a very useful feature which, in conjunction with reset monitoring ICs, will improve system reliability in unexpected power events.