if the volume is set way high then at some point yes you can melt the coil in a matter of seconds. but at your usual listening level, the overly powerful source is going to send exactly the same amount of power as any other source with enough power for that load and that voltage/listening level. the overly powerful specs are maximum specs you measure when you push the volume knob of the amp to the max or up to where the amp starts distorting when plugged into a given load. that's the only moment where you can reach and measure those values.
it's just that the less powerful amp will reach its limit sooner if you keep pushing the volume knob up. in practice that's what power specs are telling you, that the amp could go louder than the other one if you decided to.