There is nothing wrong with using a 3PH starter in 1PH service.
There is an overload heater in each of the "T" leads on the starter. This monators each phase for overload conditions. This is running overcurrent protection.Short circuit protection is provided by fuses or circuit breaker in the starter. Set the trip for the running overcurrent from the info on the motor nameplate and the overload unit will take care of the rest. To many times I have seen people add 125% to the nameplate info this makes the overload trip at 250%.