AC not big enough for Home/repost to change flair

Hi HVAC friends, I am posting because I have a unique situation in a home that I am renting in Los Angeles. I just moved on six days ago and the home is in the valley which usually has temps in the mid to high 90s all summer. I always get a home or apartment with central AC, it's like a must because the heat takes a toll on me quickly. Anyways, on moving in day my partner and I noticed that the thermostat was set at 72 but the house was at 80 degrees. As the day progressed it got up to 85 degrees in the house. The AC was running, the fan spinning, cold air coming out. I called the landlord and he said the unit was just serviced. I asked him to send a hvac tech out. He agreed annoyingly. The HVAC tech said that the system is working fine and the air is cold. He said that the system is just not enough to cool the size of the home. It has been so uncomfortable in the house for my partner and I. The landlord disagrees that is is a problem but is considering options. Can someone help me understand what the HVAC tech meant when he said we need a better and bigger system to adequately cool the house when it in the 90s? Like the house is only like 9-11 degrees cooler than outside. Like would that be a new ac unit that is outside? Or like a new furnace? Or like everything replaced? I tried to ask the HVAC tech more questions but he was not very pleasant and just kept talking over me and saying, well it is working fine just not enough in size to cool the house. When you put your hand to the vent the air is very cold, it's just not a lot of air.

Any support would be greatly appreciated. I am a complete HVAC novice haha.

Picture of the unit. American Standard Allegiancr 11 https://drive.google.com/file/d/11nCk9JC1li-mJ_Z_UnoTlsIVWHD3UBST/view?usp=drivesdk