If you fill your entire house with people elbow to elbow you might not.
Absolutely, my house isn't designed for that heat load.
20 degress is target for normal design, but most like you and I probably apply additional tonnage capacity that will compensate for peak heat. Heck if you put a 5 ton unit in a 1000 ft2 home you might get a delta T of 40 degrees.
Sure, when I design a power control room (full of medium voltage switchgear and the like), I require the units to provide the cooling at the max design ambient running 50% of the time, with one of the units shutdown. Normal for critical infrastructure that keeps a major plant running. If the ambient a day or two a year goes above our design max ambient, the units run more often but still meet our temperature requirements inside.
Again, back to my earlier point, businesses like the one question often will not spend the extra capital if they think it won't it won't be utilized.
Was this room overfilled beyond its design capacity? Was there a fire hazard due to beyond maximum occupancy allowed?
My point, and reason for responding was "HVAC system (with optimum design tonnage) evaporator coils only can produce a delta T, of about 20 degrees versus ambient." is not a true limitation. You may only get 20°F cooling across the evaporator coils, but that is from existing room temperature, not outside ambient temperature.
