I think your message got lost in the noise of the mathematics. In a sense you are right, as an RC connector, they rarely see 3 amps, and then only in short bursts.

The 3 amp limit is set by heating, and that heating is a result of the I2R losses in the connector. The higher the current (the "I" term) the more power is dissipated inside the connector at the connection point.

Over time, the resistance (the "R" term) can go up (dirty connector, many insertion/extraction cycles etc) and the I2R losses can go up. The voltage losses through the connector will increase as well.

So the engineers figure what will the heating be if you have worse case connector resistance, with a continuous current level. 3 amps is what they came up with apparently

As someone said on this thread, if you run 4+ amps through them continuous, like in a charger, they can get hot.

On one of my planes, I am running 2 batteries, with 11 servos I think. I charge about 300 mah into each battery after 2 flights. So maybe 1.2 amp/hour drain average, continuous, shared by the 2 batteries. Far below the 3 amp spec. And the average current on the worst case servo connector might be 0.2 amps continuous with 5-7 amp spikes (msec long)?

So yes these connectors are fine, IMHO. Plug and unplug one a zillion times things go bad so I just clip them and replace them periodically.