1) Having three-phase power allows you to connect larger and higher draw appliances. They’ll also run better due to having sufficient power load to supply them.
2) Three-phase power allows for more appliances/devices to be connected at the same time, while also allowing the higher draw appliances to be connected separate from the lower draw ones.
3) Three-phase power also allows for a more consistent supply of power to your appliances. Due to the nature of the phases of power, for a fraction of a second at regular intervals, some devices can experience moments where there is 0 voltage available. With three phase power, even at a moment where one circuit is at 0, the other two are still providing electricity [might need a diagram to help with this bit].
4) Three-phase power does not increase your energy bill at all compared to single-phase power.
5)Circuits have a far less chance of tripping due to a lack of voltage when running with three-phase power.