I don’t understand your point.

If the speaker is 4 ohms @25 watts you would use 5.7v for 1/3 power.

IMO this is a good way to go because it is a very simple approach.

1/3 power is in no way ambiguous but you do have to calculate it correctly. You can’t calculate the voltage without using the resistance. This is clearly stated in the links you posted and there is even a program the will do the calcs for you if you plug in the numbers.

If you run a 4 ohm 25w speaker at 8v it will dissipate about 16w which is 2x the recommended value so yes it may get hot because it is dissipating 2/3 rated power not the recommended 1/3.