That multiplication factor is easily negative though, unless you specifically design the antenna to have gain. And a 20dB gain like you are referring to is a very high gain antenna already that will have to be designed and built quite carefully.
My point was that it is ridiculously easy to get it all wrong and suddenly achieve unintendedly strong radiated power. Again, it was a crude example of a thought experiment with a wide, wild number of variables to be considered.
