That's not even close to correct. At the design lowest temperature (if <15°C), the very best get 2 COP, but most are 1.5 or lower. The problem is you have to accommodate the worst case.

The average of installed units is closer to 2.0 COP average, unfortunately. Multi-head units really drive down efficiency. A single-head Gree Sapphire can do 4-5 COP on average and that's the best you can get, so still nowhere near your guess.