Possibly Ignorant Power Question

Two possible reasons.  First is if it's a tube amp.  Most use transformers so the different taps all put out the same wattage.  Second is the amp is current limited.

Keep it simple. Forget power, forget ohms. Focus on speaker sensitivity. When speaker sensitivity is high this is telling you they can be easily driven by a wide range of amplifiers regardless of power. A speaker with 98dB sensitivity for example will play 98dB at 1m with only one watt. Even further away where you sit and listen that is pretty loud. With just one watt. It should be pretty obvious when using this speaker it is totally irrelevant if amplifier power doubles. All this stuff becomes irrelevant.  

The only reason it matters is many audiophiles still have not figured out all they have to do is ignore any speaker so power hungry it is unable to put out at least 92dB with 1 watt. They do this left and right, and once you get clued into what is going on you will notice all the people complaining about power and searching for amps and going on and on about what amp goes with what speaker, they are always using speakers less than 92dB sensitivity. Vast majority of the time for sure. And the more power hungry the speakers are the more they go on and on about it. Try and find the Martin Logan owner who says wow I can use any amp and my speakers sound great! No such thing.

The reason for this is very simple, it is that power and sound are log functions. Simple if you know math I mean. Sound seems to increase linear because we use dB which are exponential. So while 3dB sounds only a little bit louder, it is twice the power. Ignore my advice and buy a 89dB speaker you don't need a little more power you need twice as much. This is why all these people obsessed with power doubling as impedance drops. They never learned that with amps it is always the speaker that comes first - do don't blow it!

The real measure of an amplifiers ability to drive speakers is current. Current is not a standard measurement, but you can indirectly measure it by measuring the watts at different impedance. Regardless of what speaker you are using you want the one able to produce more current. The closer to watts doubling between 2, 4, 8... the better. I have had massive amps driving speakers not requiring the power and given all things equal the more powerful the better the sound. So for instance my Pass x350 sounded better than a Pass x250.
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There are specially speakers made to be driven by flea powered amps... I assume if you were in that category you would know it.
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Conversely some speakers require lots of power. They don’t do this to be difficult, they have a reason. This is overly simplified. Consider a speaker with a light weight magnet and light material to pull the cone back... it pushes the cone around easily. It also requires little power to do so. But the cone is not stiff and it takes it’s time coming back once extended. So the sound is flabby. Now stiffen the cone and add massive magnets... it requires much more power... but it makes very fast excursions and the cone doesn’t deform while trying to do different sounds at the same time. Much more accurate sound. .
so it is important to find speakers you like and power with at least enough. From my experience if you have a choice of two identical sounding amp the one with greater current grabs the cones better and makes them do what they are supposed to be doing.