Will feeding your amplifier less power reduce it's output? Sure. Would making that amplifier do less amplifying, not 'work' as hard, mean that it could last longer? That's a pretty safe bet too, less heat build up being just one of the reasons for that. Is the ratio of the input power to the output power linear, a 1/4 of the input meaning a 1/4 of the output? No, it isn't. You can make a fairly close guess by thinking of it as being linear, directly proportional, but it just doesn't work that way for a number of reasons, circuit design being just one of them. Transistors and tubes are not 'linear' devices, their amplification isn't a 'straight' line on a graph, but a 'curve' that starts off sort of 'flat' and increases it's upward climb to a steeper angle as the amount of power fed to it increase. At some point it get's to the point of very little gain in power in relation to the amount of power being fed to it. Somewhere on that curve the rate of increase get's to be almost linear. Increase input and the output increases at a proportional rate. That portion of the device's amplification curve is the 'best' place to operate that particular device. The amplification is being done in the most efficient manner and is a good representation of the signal being fed to that device. There are other sections of that amplification curve that can produce a much larger output when compared to the input, but that is only 'good' when the 'quality' of the output doesn't matter, it isn't being distorted by being amplified. Works great for CW, but for voice modes it's just terrible. A "What did he say?", kind'a thing.
Each particular device has a different amplification 'curve', they all are NOT the same. Even two of the same devices are different a little bit, so things have to be adjusted for each particular device. Two transistors, or tubes, of the same model are going to be very slightly different. In most cases it probably won't even be noticeable, but there's a difference. So, if you 'assembly-line' an amplifier, sometimes you end up with a 'dud' unless you tune each amplifier separately according to the device(s) in that amplifier. Almost no one ever does that unless there are gross differences. It isn't ever as simple as it seems like it ought to be.
Amplifiers can't tell that there are 'parts' to a signal, they only know that there's a total 'lump' of input that it is supposed to make 'larger'. Those 'parts' of a signal refer to the carrier and applied modulation for an AM signal. An amplifier can't 'adjust' that carrier/modulation, it can only amplify what's presented to it. It goes by -total- signal. The transmitter that does that feeding to the amplifier is supposed to handle that carrier to modulation, keep the ratio in the right proportion to produce a good signal. So, if you want to change that carrier/modulation ratio (change the percentage of modulation) the transmitter is where to do it. So what's the deal about tuning an amplifier with just a carrier/'dead key'? The reason is it's easier to do 'sort of right' than it is to do it right. Most people have no way of producing a steady, modulated signal to do testing/tuning with. That 'steady' type input can't be done by voice, whistling, it's just not steady enough. And then, if the amplifier is being operated in the 'linear' portion of it's amplification curve, just using a carrier will get you 'close'. [Does any of that sound familiar?
Is that a good technical explanation? Good grief no! But it get's the general idea across.]