The pressure at which the fan turns on will have some effect on the cooling efficiency, but that is not why it is there. It is to protect the system from excessive high side pressure.

At this point you need to do a performance test. This involves measuring temperature in front of the condensor and temperature at the inside cooling vent. This is after stabilization of the system running full cooling setting and max fan speed and with engine at about 1500RPM. You should also monitor low and high side pressure. With these four parameters; low side psi, high side psi, condensor ambient and inside vent temps, we can go to the tables to see where we're at.

Also the low and high side pressures will give an idea about the condition of the expansion valve.

Have a great day,