every car A/C has an evaporator thermostat to cut out the compressor when the evaporator reaches near freezing. This is to prevent it becoming a big block of ice. At low fan speed the evaporator does not absorb heat fast enough hence remains cooler and hence the tstat switches off the compressor earlier.
Anyway,,, I always had the habit of first exhausting the car of hot air by opening all doors, then I use the A/C on full fan speed for a few minutes, 10 or 15, then switch to low - This maintains very comfortable temperature of 24C in the cabin. The A/C job is to "condition" the air not make the car a freezer. You can buy an icecream truck for that.
Never had any major A/C problems and always had quick cool down time. I also made sure my car does not have air leaks anywhere, the biggest ones are usually the door rubbers or the plastic liner behind the door panels - They can allow a lot of air in the cab.
I also made sure the centre vents are pointing up, this causes air to shoot towards the back of the car (rear seats) it will eventually fall right on the passengers as cold air drops. I did the exact opposite for heat, aim at feet and defrost to evenly heat the cab. Aiming the vent at your face is useless.