I don't know how to make this more clear, and there really is nothing complicated about it. Ohms law is ohms law. All portions of the pie chart are equal. That's how he proved his law. When resistance is static, to change power, you change volts. When resistance is fixed, if you change volts, you change power. They are equal. It is the exact same thing. Marketing does not disprove ohms law.
We're aware that they're related via the equation, but that does not make them equal.
Y = X^2 for example. Y is always directly related to X, but X and Y are not equal (except at zero, of course, but even so they're being measured on different axes that just happen to share the same point right there).
It's a matter of design, not of any electrical difference. If I let you set Y and adjust my X accordingly, you can double Y and be assured that Y actually does double. That's handy if what you're doing relies on output-Y to perform a function.
If you're relying on output-Y but adjusting X, doubling Y becomes a more difficult proposition. You have to remember to adjust X upward by the square root of 2 to double Y. That's inconvenient and makes the user think.
Over time, it's not hard to adjust to VV and most of us have done so. For new users, VW is much easier as the reaction at the atty is linear and the little chip in there does the square root of two thing for me to the voltage. They don't have to think about it.
Marketing does not disprove ohms law. Ohms law is proven and can not be disproven. - Further, I'm baffled how it is those who are convinced that VW is different than VV also seem to forget the important part is the first V = variable. Variable is the important part. Otherwise, fixed regulators would have won the day and we wouldn't have all of these wonderfully functional and fancy
devices.
Well, actually, I could adjust the equation appropriately and make anything I want the variable to solve for.
Interestingly, I built emergency lights for Christmas from some high-powered LEDs and a multi-input capable source. The
amperage is regulated. The
voltage can vary anywhere across a reasonable range it wants to (6 to 15 volts input). Light output remains the same, there's no difference in power consumed at the LED.
Another set of gifts involved powering a chip using a voltage far too low for it (in other words, it wouldn't work).
Same with a mod. Ohm's Law may be consistent and predictable for all linear resistors, but our mods don't strictly-speaking work by Ohm's Law. There are microchips in there that are fully capable of being as non-linear as they want, just like the one on my desk. It's clamping its output to 10 milliamps on pin 3 even though the (non-linear)
device located there will happily pull down all the amps it can get at the voltage at which it's running (which would destroy it in microseconds). The microchip does not care and is efficiently doing its job, and making my little device do its job without bursting into flame.
So really, I can build you something that varies any part of the equation you want, and produces whatever answer you want.