With the mouse or the trackpad of the computer, you can only click on something with one hand. With the DJ controller, you can perform several actions at the same time, such as switching on an effect and adjusting the volume at the same time. This helps a lot when a fast song is playing.
The DJ controller gives an analogue output signal to an amplifier so that the music is heard better. This is very important for parties in clubs.
With the DJ controller, you don't have to look at the laptop as much because you get feedback from your fingers when you have turned a knob. It makes your work much easier and you look more professional. It also gives you time to observe the audience and notice their mood.
A laptop has only one audio output, which you will use for the speakers at the party. So you have no way to preview the tracks with your headphones. The DJ controller still has an audio output that you can connect your headphones to and control the volume independently.
Since you can't preview the tracks without the DJ controller, you can't pick a song that fits the mood during the party. So you can't find the place in the new song where you want to start it.