Are you talking solid state or tube amplifiers?
Scotty
Solid State could use an output transformer just like Vacuum State does; it's just that most don't (it's kind of expensive). McIintosh SS amps do, for example, and it was quite common in the early days of Solid State. If there's a power transformer, then (assuming there are taps, and the load is reasonably matched to the tap) it's the same power output into any of the available loads.
I also don't agree with the 60% thing. What a SS amp (that does not use an output transformer) can deliver into varying loads depends on how it's constructed. If the power supply is adequate and the devices are suitably rated and the unit can dissipate the required heat, it should double or half ... 1 volt into 8 ohms is 2 volts into 4 ohms.
Amplifiers that really do deliver less than 2x into a 4 ohm load have some limitation that's preventing that, or it's using a design where that's not feasible. Typically it's the power supply, because that's often the most expensive area to build really robust, but it could be something else.
It could even be just the specification itself ... amps must meet the UL or CSA safety test regimen for every power rating and load they specify in the spec sheet, and those include limits on how hot it can get because it's a consumer product sold for use in the home (even if it could run hotter safely). If it won't meet a low-impedance UL test, all you have to do is not rate it for that load, and in that case you can pass the test and get certified.
Perhaps it's even de-rated or simply not rated into a given load because it can't meet the UL test, but in reality if you ask it to, away it goes for the short periods we ask amps to produce transients playing music. There are lots of possible scenarios.
There's a saying when you are doing survival or navigation training: "The map is not the territory". The audio corollary is: The spec sheet is not the performance.
Since everything costs money, different designers make different choices toward different goals. Unless you're building those five and six-figure amps that Stereophile keeps insisting really exist, there has to be some compromise between value and performance somewhere. I don't mean to suggest that an amp that does deliver, say, 160% of it's rated 8 ohm continuous power into a 4 ohm load is somehow inadequate ... money spent on something you can't use is money wasted, as far as the user is concerned. Match the amp to your power needs and the intended load, and go listening.
Most SS amplifiers respond to a 4 Ω load with an average of 60% more power output compared to how they measure with an 8 Ω load. But what happens when a 12 ohm or higher load is applied? Does the power output decrease?
The amp could be designed to work optimally into a 12 ohm load, and deliver the best power into that load. It's just that it isn't the way we've customarily done it.
