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.

Good explanation with last answer.  Sufficient current whatever the load (which varies over time with speakers depending on what is being sent to them) is what's important.  So the doubling of watts as ohms halve is a useful rule of thumb that can give you some confidence that the amp will be able to produce sufficient current.  The speaker sensitivity of course plays in as also mentioned, but if looking just at the amp specs, the "doubling" is a nice feature to have at a quick glance.

You ask about 200 watts @ 8, 4, and 2 ohms. That is saying you will have 200 watts available AT 8, 4 or 2 ohms. Nothing less. BUT there is most likely MORE at 4 and 2 ohms..

OP you have to read through the word salad.. BUT That is all that is being said. 

The doubling of wattage is a typology. Nothing more, nothing less.

You will hear class A is all the rage, BUT when you crank most type a amps all the way up, they REALLY start to distort.. Run out of gas, they (Class A) have their own SET of problems :-).  Are they the best?

The same question your asking offers the same answer.
What can you afford?
What do you like?
Are there environmental issues, like HEAT, or kids and animals?

Understand, some amps are just as good SQ wise as others but that may not be what YOU like..

Sound Quality is in the EARS of the beholder.

Toes in the water, AY?

I don't think double the power output at 4Ω  over 8 is much of an indicator of how good an amplifier is... sure it's easier to make one that doesn't double but there's no reason why one that does would sound better.
My advice would be not to go for an amplifier that's more powerful than you actually need. Most if not all amplifiers sound better running at the top half of their rated output so if you go for something four times as powerful as you need then the cost of that unused power is a reduction in sound quality. The other thing is that most volume controls sound worse the more you turn them down as well, with the exception of decent resistor based attenuators. I did a short blog post on amplifier power vs loudness that might be interesting.

Keep in mind that a manufacturer's spec of doubling into 4 ohms is often not accurate when the amp is actually tested.  For example, the specs may say 70wpc into 8 ohms and 140wpc into 4 ohms.  The actual tests could show something like 110wpc into 8 ohms and 150 wpc into 4 ohms.  Technically, the amp exceeds its specs, but it doesn't come close to doubling into 4 ohms.  

"...It should be pretty obvious when using this speaker it is totally irrelevant if amplifier power doubles. All this stuff becomes irrelevant..."
Unless you like speakers like big Magnepans and others.   

"...Try and find the Martin Logan owner who says wow I can use any amp and my speakers sound great! No such thing..."
I'm one. The M-L Electromotion ESL is 91db efficient and I drive them very well with my 25wpc tube amp. Every rule has an exception...I do agree on your efficient speaker premise, it makes life easier for sure.  

@smrex13 I hear you but the one I really like was tested by Stereophile and exceeds both 4 and 8 ohm ratings by a decent margin.

@millercarbon I'd like to know what else you think is low impedance besides Tekton?

@oldhvymec and others....rest assured i'm not making a decision strictly off of this, it was more curiousity. Mcintosh is the example here.  The MA352 hybrid integrated is rated (from memory) @200/8 and 320/4 ohm respectively.  Yet the more expensive MA9000 is 300@any impedance.  Why not tout it as 300/8 and 600/4 or whatever it is?  It does seem to correlate to their autoformer (?)  products.  

mtbiker29 OP
So the question is why do some manufacturers then have ratings such as "200W@8,4,2 ohms

vinylzone25 posts04-10-2021 11:48pmTwo 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.

Mac’s also have those sort of specs because their Solid State amps have output transformers, and they can’t even come close to doubling for each halving of impedance, I’ve never like their sound.
The only I ever like of their was the original tube MC240 on Quad 57's
https://kenrockwell.com/audio/mcintosh/mc240.htm

Cheers George